{"id":169,"date":"2011-09-02T22:44:22","date_gmt":"2011-09-02T20:44:22","guid":{"rendered":"http:\/\/blog.copcea.ro\/?p=169"},"modified":"2017-04-02T13:23:43","modified_gmt":"2017-04-02T11:23:43","slug":"169","status":"publish","type":"post","link":"http:\/\/blog.copcea.ro\/?p=169","title":{"rendered":"Problem\u0103 de matematic\u0103"},"content":{"rendered":"<div class=\"02a7dab7e6fe5a0fbf433999ff85f046\" data-index=\"1\" style=\"float: none; margin:10px 0 10px 0; text-align:center;\">\n<script type=\"text\/javascript\"><!--\r\ngoogle_ad_client = \"ca-pub-2343103762362018\";\r\n\/* 336x280 *\/\r\ngoogle_ad_slot = \"8815738048\";\r\ngoogle_ad_width = 336;\r\ngoogle_ad_height = 280;\r\n\/\/-->\r\n<\/script>\r\n<script type=\"text\/javascript\"\r\nsrc=\"http:\/\/pagead2.googlesyndication.com\/pagead\/show_ads.js\">\r\n<\/script>\n<\/div>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p><span style=\"color: #ffff00;\"><strong>Preambul<\/strong><\/span><\/p>\n<p>Orice persoan\u0103 are nevoie \u00een via\u021b\u0103 de un pol fix, de un punct de sprijin \u00een care s\u0103 se \u00eencread\u0103 \u00een mod absolut, \u00een orice moment \u0219i \u00een orice condi\u021bii.<\/p>\n<p>Unii oameni fac apel la religie, al\u021bii fac apel la alte persoane de care sunt dependente, al\u021bii cred \u00een Steaua Polar\u0103 sau doar \u00een stele \u00een general, al\u021bii cred \u00een bani, unii cred \u00een onestitate, al\u021bii \u00een \u00een\u0219el\u0103torii, unii cred \u00een valorile spirituale, al\u021bii \u00een valorile materiale&#8230;indiferent de situa\u021bie, fiecare crede \u00een ceva.<\/p>\n<p>Via\u021ba ne arat\u0103 deseori c\u0103 polurile fixe \u00een care credem nu sunt chiar at\u00e2t de fixe, deseori ne modific\u0103m crezul pentru c\u0103 polul \u00een care credem nu ne mai satisface, nu mai &#8220;func\u021bioneaz\u0103&#8221;. Deseori credem c\u0103 nici m\u0103car nu ar putea exista un pol fix p\u00e2n\u0103 c\u00e2nd altcineva nu \u00eel descoper\u0103 \u00een locul nostru \u0219i ne deschide \u0219i nou\u0103 ochii&#8230;<\/p>\n<p>Eu cred \u00een&#8230; Pi=3.1415926&#8230;.\u00een e=2.71828182&#8230; constante universale pe care nu le modific\u0103 nici un fel de regul\u0103 uman\u0103 \u0219i nici un fel de comportament&#8230;<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p><span style=\"color: #ffff00;\"><strong>Preamble<\/strong><\/span><\/p>\n<p>Every individual needs in life a fixed pole, a point of support which he\/she will trust absolutely, at any moment and in every conditions.<\/p>\n<p>Some people trust religion, some trust other people whom they depend on,some believe in the Northern Star or in any other star, some believe in money, some in honesty while others in scams, some believe in spiritual values while others believe in material values&#8230;no matter the situation, everybody believes in something.<\/p>\n<p>Life shows us often that the fixed poles we believe in are not so fixed, often we modify our belief because the pole we used to trust isn&#8217;t satisfactory anymore, it doesn&#8217;t &#8220;work&#8221;. Often we believe a fixed pole can&#8217;t even exist until someone else discovers it for us and opens our eyes &#8230;<\/p>\n<p>I believe in&#8230; Pi=3.1415926&#8230;.in e=2.71828182&#8230; universal constants no human rule and no kind of behavior can alter &#8230;<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p><span style=\"color: #ffff00;\"><strong>Pr\u00e9ambule<\/strong><\/span><\/p>\n<p>Toute personne a besoin d&#8217;un p\u00f4le fixe dans la vie, d&#8217;un point de support auquel il\/elle fera confiance absolument, en tout moment et n&#8217;importe quelles les conditions.<\/p>\n<p>Des gens font appel \u00e0 la religion, d&#8217;autres font appel \u00e0 d&#8217;autres personnes desquelles elles d\u00e9pendent, des gens croient \u00e0 l&#8217;Etoile du Nord, d&#8217;autres dans les \u00e9toiles tout simplement, des uns croient en l&#8217;argent, des uns croient en l&#8217;honn\u00eattet\u00e9 tandis que d&#8217;autres en l&#8217;ensorcelage, des uns croient dans les valeurs spirituelles tandis que d&#8217;autres croient dans les valeurs mat\u00e9rielles&#8230;n&#8217;importe la situation, chacun croit en quelque chose.<\/p>\n<p>La vie nous montre souvent que les p\u00f4les fixes dans lesquels nous croyons ne sont pas si fixes que \u00e7a, souvent on modifie notre croyance parce que le p\u00f4le dans lequels nous croyons ne nous satisfait plus, il ne &#8220;fonctionne&#8221; plus. Souvent on ne croit plus qu&#8217;il puisse y avoir de p\u00f4le fixe jusque quelqu&#8217;un d&#8217;autre le d\u00e9couvre pour nous et r\u00e9ussit \u00e0 nous ouvrir les yeux&#8230;<\/p>\n<p>Je crois en&#8230; Pi=3.1415926&#8230;.en e=2.71828182&#8230; constantes universelles que nul r\u00e8glement ni comportement humain peut modifier&#8230;<\/p>\n<\/div>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p><span style=\"color: #ffff00;\"><strong>Problem\u0103 de matematic\u0103<\/strong><\/span><\/p>\n<p>Badea \u0219i Pr\u00e2slea aveau o turm\u0103 de oi, iar via\u021ba lor se ducea \u00een jurul turmei, care le d\u0103dea toate cele necesare pentru traiul zilnic.<\/p>\n<p>\u00centr-o zi, Badea \u00eei spuse lui Pr\u00e2slea:<\/p>\n<p>&#8211; M\u0103i Pr\u00e2sleo, ap\u0103i iaca io v\u0103d c\u0103 nu om mai putea tr\u0103i de pe urma turmei, m\u0103i, c\u0103 se scumpe\u0219te iar\u0103 kilu&#8217; de oaie !<\/p>\n<p>&#8211; A\u0219a \u00eei, Bade, am v\u0103zut \u0219i io c\u0103 str\u00e2ngem cureaua de nu mai am g\u0103uri la ea!<\/p>\n<p>&#8211; Ap\u0103i Pr\u00e2sleo, cat c\u0103 mai bine vindem oile \u0219i ne facem o firm\u0103 de, cum \u00eei zice, soft din \u0103la pentru calculatoare, c\u0103 toat\u0103 lumea are azi un calculator \u0219i or avea \u0219i ei nevoie de ceva soft nou!<\/p>\n<p>&#8211; Bade, matale e\u0219ti fratele mai mare \u0219i io oi face cum spui matale!<\/p>\n<p>Zis \u0219i f\u0103cut, se duc fra\u021bii la t\u00e2rg \u0219i v\u00e2nd toate oile, \u0219i iau pe o oaie c\u00e2te oi aveau. Se \u00eentorc la st\u00e2n\u0103 iar Badea zice:<\/p>\n<p>&#8211; Pr\u00e2sleo, oi fi io fratele mai mare, d-ap\u0103i noi suntem fra\u021bi \u0219i fr\u0103\u021be\u0219te om \u00eemp\u0103r\u021bi totul!<\/p>\n<p>&#8211; Bine, Bade, cum zici matele a\u0219a om face!<\/p>\n<p>&#8211; Ap\u0103i hai sa \u00eemp\u0103r\u021bim: zece mie, zece \u021bie, zece mie, zece \u021bie, zece mie, zece \u021bie, zece mie, zece \u021bie&#8230;&#8230;. zece mie, iar\u0103 \u021bie&#8230;na de-aici ce-o r\u0103mas \u0219i i\u021bi dau \u0219i bri\u0219ca mea ca s\u0103 fim chit. \u00cei bine, Pr\u00e2sleo?<\/p>\n<p>&#8211; Ap\u0103i o fi bine, Bade, dac\u0103 a\u0219a zici matale!<\/p>\n<p><strong>C\u00e2t cost\u0103 bri\u0219ca? <\/strong><\/p>\n<hr size=\"2\" \/>\n<p><span style=\"color: #ffff00;\"><strong>Rezolvare:<\/strong><\/span><\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p><span style=\"color: #ffff00;\"><strong>Mathematics Problem<\/strong><\/span><\/p>\n<p>Two shepherds brothers had a flock of sheep. Their life revolved around the flock which gave them in return everything they needed for everyday life, but things got slowly worse and worse.<\/p>\n<p>One day, the big brother told the little one:<\/p>\n<p>&#8211; Little brother, I guess the flock can&#8217;t support us anymore!<\/p>\n<p>&#8211; Big brother, I reckon it is like you say!<\/p>\n<p>&#8211; Little brother, I think we&#8217;d better sell the flock and incorporate a software company. Everybody owns a computer nowadays and they sure need new software!<\/p>\n<p>&#8211; Big brother, you are the smart one, we&#8217;ll do as you say!<\/p>\n<p>The two brothers went then to sell the flock and they took for one sheep the number of sheep they had. They went back home and the big brother says:<\/p>\n<p>&#8211; Little brother, I may be the Big brother, but we are still brothers and we&#8217;ll divide everything in half!<\/p>\n<p>&#8211; Whatever you say, big brother!<\/p>\n<p>&#8211; OK, let&#8217;s count: ten for me, ten for you, ten for me, ten for you, ten for me, ten for you,&#8230;. ten for me, and take this rest to which I will add my knife to be fair and square. Is it OK, little brother?<\/p>\n<p>&#8211; Big brother, everything is fine!<\/p>\n<p><strong>How much is the knife? <\/strong><\/p>\n<hr size=\"2\" \/>\n<p><span style=\"color: #ffff00;\"><strong>Solution:<\/strong><\/span><\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p><span style=\"color: #ffff00;\"><strong>Probl\u00e8me de Math\u00e9matiques<\/strong><\/span><\/p>\n<p>Deux bergers avaient un troupeau de moutons, leur vie tournait autour du troupeau et le troupeau leur donnait, en retour, tout ce qu&#8217;ils avaient besoin pour leur vie quotidienne.<\/p>\n<p>Un jour, l&#8217;a\u00een\u00e9 dit au jeune fr\u00e8re:<\/p>\n<p>&#8211; Mon jeune fr\u00e8re, je vois que le troupeau n&#8217;apporte plus comme avant et il est de plus en plus difficile de vivre!<\/p>\n<p>&#8211; Grand fr\u00e8re, je pense bien que c&#8217;est comme tu le dis!<\/p>\n<p>&#8211; Petit fr\u00e8re, je pense qu&#8217;on devrait vendre le troupeau et ouvrir une soci\u00e9t\u00e9 d&#8217;informatique. Tout le monde a un ordinateur ces jours-ci et ils doivent bien avoir besoin de nouveaux logiciels!<\/p>\n<p>&#8211; Grand fr\u00e8re, tu est le plus sage, nous ferons comme tu le dis!<\/p>\n<p>Les deux fr\u00e8res vendirent le troupeau et il touch\u00e8rent pour un mouton le nombre de moutons dans le troupeau. Ils revenirent chez eux et le grand fr\u00e8re dit:<\/p>\n<p>&#8211; Petit fr\u00e8re, je suis l&#8217;a\u00een\u00e9 mais \u00e7a ne nous fait pas moins fr\u00e8res, nous allons tout diviser par deux!<\/p>\n<p>&#8211; Comme tu dis, grand fr\u00e8re!<\/p>\n<p>&#8211; Allez, on va compter: dix pour moi, dix pour toi, dix pour moi, dix pour toi, dix pour moi, dix pour toi, dix pour moi, et prend ce qui reste. Je vais ajouter mon couteau au reste pour qu&#8217;on soit quitte. Est-ce bien?<\/p>\n<p>&#8211; C&#8217;est bien, si tu le dis, grand fr\u00e8re!<\/p>\n<p><strong>Combien co\u00fbte le couteau? <\/strong><\/p>\n<hr size=\"2\" \/>\n<p><span style=\"color: #ffff00;\"><strong>Solution:<\/strong><\/span><\/p>\n<\/div>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Not\u0103m astfel:<\/p>\n<p>N\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 num\u0103rul de oi din turm\u0103<\/p>\n<p>P\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Banii \u00eencasa\u021bi pe oi<\/p>\n<p>M\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 num\u0103rul de m\u00e2ini de c\u0103te dou\u0103zece de lei (zece mie, zece \u021bie)<\/p>\n<p>R\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 restul dat lui Pr\u00e2slea<\/p>\n<p>K\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 costul cu\u021bitului<\/p>\n<p>Putem scrie urm\u0103torul sistem de ecua\u021bii :<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>Notations:<\/p>\n<p>N\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the number of sheep in the flock<\/p>\n<p>P\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the money the two brothers got on the sheep<\/p>\n<p>M\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the number of hand of twenty pounds (ten for me, ten for you)<\/p>\n<p>R\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the rest the little brother took<\/p>\n<p>K\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the cost of the Knife<\/p>\n<p>We can write down the following equations:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>Notations:<\/p>\n<p>N\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 le nombre de moutons dans le troupeau<\/p>\n<p>P\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 le prix de tous les moutons<\/p>\n<p>M\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 le nombre de mains de vingt francs (dix pour moi, dix pour toi)<\/p>\n<p>R\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 le reste touch\u00e9 par le petit fr\u00e8re<\/p>\n<p>K\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 le co\u00fbt du couteau<\/p>\n<p>Nous pouvons \u00e9crire les \u00e9quations suivantes:<\/p>\n<\/div>\n<p>P=N<sup>2<\/sup><\/p>\n<p>N=20M+10+R<\/p>\n<p>R+K=10<\/p>\n<p>0&lt;R&lt;10; 0&lt;K&lt;10<\/p>\n<p>R,K,M,N,P \u03f5 <strong>N<\/strong><\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Se \u0219tie c\u0103 orice num\u0103r X poate fi scris sub forma canonic\u0103 urm\u0103toare:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>We know any number X can be written in the following canonical form:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>On sait que tout nombre X peut \u00eatre \u00e9crit sous la forma canonique suivante:<\/p>\n<\/div>\n<p>X= x<sub>0<\/sub>10<sup>0<\/sup>+x<sub>1<\/sub>10<sup>1<\/sup>+x<sub>2<\/sub>10<sup>2<\/sup>+&#8230;+x<sub>n<\/sub>10<sup>n<\/sup><\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Calcul\u0103m X<sup>2<\/sup>:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>We compute X<sup>2<\/sup>:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>On calcule X<sup>2<\/sup>:<\/p>\n<\/div>\n<p>X<sup>2<\/sup> = x<sub>0<\/sub><sup>2<\/sup>10<sup>0<\/sup>+x<sub>1<\/sub><sup>2<\/sup>10<sup>2<\/sup>+&#8230;+x<sub>n<\/sub><sup>2<\/sup>10<sup>2n<\/sup> + 2x<sub>0<\/sub>x<sub>1<\/sub>10<sup>2<\/sup>+&#8230;2x<sub>0<\/sub>x<sub>n<\/sub>10<sup>n<\/sup> + 2x<sub>1<\/sub>x<sub>n<\/sub>10<sup>n+1<\/sup> + &#8230;.<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Grup\u0103m astfel:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>We group this way:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>On groupe ainsi:<\/p>\n<\/div>\n<p>X<sup>2<\/sup> = x<sub>0<\/sub><sup>2<\/sup>10<sup>0 <\/sup>+ 20(5x<sub>1<\/sub><sup>2<\/sup>+&#8230;+5x<sub>n<\/sub><sup>2<\/sup>10<sup>2n-2<\/sup> + x<sub>0<\/sub>x<sub>1<\/sub>10<sup>1<\/sup>+&#8230;x<sub>0<\/sub>x<sub>n<\/sub>10<sup>n-1<\/sup> + x<sub>1<\/sub>x<sub>n<\/sub>10<sup>n<\/sup> + &#8230;.)<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Dac\u0103 x<sub>0<\/sub><sup>2<\/sup>&gt;20, not\u0103m x<sub>0<\/sub><sup>2<\/sup> = 20A + B<\/p>\n<p>unde B&lt;10<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>If x<sub>0<\/sub><sup>2<\/sup>&gt;20, we note x<sub>0<\/sub><sup>2<\/sup> = 20A + B<\/p>\n<p>where B&lt;10<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>Si x<sub>0<\/sub><sup>2<\/sup>&gt;20, on note x<sub>0<\/sub><sup>2<\/sup> = 20A + B<\/p>\n<p>o\u00f9 B&lt;10<\/p>\n<\/div>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>\u00cen acela\u0219i timp, \u0219tim c\u0103:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>At the same time, we know that:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>En m\u00eame temps, l&#8217;on sait que:<\/p>\n<\/div>\n<p>N=20M+10+R<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>\u0219i:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>and:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>et:<\/p>\n<\/div>\n<p>N<sup>2<\/sup> = x<sub>0<\/sub><sup>2<\/sup>10<sup>0 <\/sup>+ 20(5x<sub>1<\/sub><sup>2<\/sup>+&#8230;+5x<sub>n<\/sub><sup>2<\/sup>10<sup>2n-2<\/sup> + x<sub>0<\/sub>x<sub>1<\/sub>10<sup>1<\/sup>+&#8230;x<sub>0<\/sub>x<sub>n<\/sub>10<sup>n-1<\/sup> + x<sub>1<\/sub>x<sub>n<\/sub>10<sup>n<\/sup> + &#8230;.)<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\nNot\u0103m\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\nWe note\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\nOn note\n<\/div>\n<p>S=5x<sub>1<\/sub><sup>2<\/sup>+&#8230;+5x<sub>n<\/sub><sup>2<\/sup>10<sup>2n-2<\/sup> + x<sub>0<\/sub>x<sub>1<\/sub>10<sup>1<\/sup>+&#8230;x<sub>0<\/sub>x<sub>n<\/sub>10<sup>n-1<\/sup> + x<sub>1<\/sub>x<sub>n<\/sub>10<sup>n<\/sup> + &#8230;.<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\nAdic\u0103\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\nMeaning\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\nC&#8217;est \u00e0 dire\n<\/div>\n<p>N<sup>2<\/sup> = x<sub>0<\/sub><sup>2<\/sup>+20S <\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\ndac\u0103\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\nif\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\nsi\n<\/div>\n<p> x<sub>0<\/sub><sup>2<\/sup>&lt;20<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>\u0219i:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>and:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>et:<\/p>\n<\/div>\n<p>N<sup>2<\/sup> = 20A+B+20S = B+20(A+S) <\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n dac\u0103\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n if\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n si\n<\/div>\n<p> x<sub>0<\/sub><sup>2<\/sup>&gt;20<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Astfel, conform celor de mai sus, avem:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>According to the above, we have:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>En conformit\u00e9 avec ci-dessus:<\/p>\n<\/div>\n<p>10+R= x<sub>0<\/sub><sup>2 <\/sup><\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n dac\u0103\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n if\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n si\n<\/div>\n<p> x<sub>0<\/sub><sup>2<\/sup>&lt;20<\/p>\n<p>10+R=B<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n dac\u0103\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n if\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n si\n<\/div>\n<p> x<sub>0<\/sub><sup>2<\/sup>&gt;20<\/p>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>Calcul\u0103m valorile posibile ale nota\u021biilor func\u021bie de valoarea lui x<sub>0<\/sub>:<\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>We compute all possible values of the above notations, function of x<sub>0 <\/sub>value:<\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>On calcule toutes les valeurs possibles des notations ci-dessus en fonction de la valeur de x<sub>0<\/sub>:<\/p>\n<\/div>\n<pre><strong>x<sub>0<\/sub>     x<sub>0<\/sub><sup>2<\/sup>     A\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B\u00a0\u00a0\u00a0\u00a0\u00a0 10+R\u00a0\u00a0\u00a0\u00a0 R\u00a0\u00a0\u00a0\u00a0 C<\/strong><\/pre>\n<pre>1\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 \u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>- <\/strong> <strong>  -<\/strong><\/pre>\n<pre>2\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>- <\/strong> <strong>  -<\/strong><\/pre>\n<pre>3\u00a0\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>- <\/strong> <strong>  -<\/strong><\/pre>\n<pre>4\u00a0\u00a0\u00a0\u00a0 16\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16\u00a0\u00a0\u00a0\u00a0\u00a0 16\u00a0\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0 4<\/pre>\n<pre>5\u00a0\u00a0\u00a0\u00a0 25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>- <\/strong> <strong>  -<\/strong><\/pre>\n<pre>6\u00a0\u00a0\u00a0\u00a0 36\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16\u00a0\u00a0\u00a0\u00a0\u00a0 16\u00a0\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0 4<\/pre>\n<pre>7\u00a0\u00a0\u00a0\u00a0 49\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>- <\/strong> <strong>  -<\/strong><\/pre>\n<pre>8\u00a0\u00a0\u00a0\u00a0 64\u00a0\u00a0 \u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>- <\/strong> <strong>  -<\/strong><\/pre>\n<pre>9\u00a0\u00a0\u00a0\u00a0 81\u00a0\u00a0 \u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>-   <\/strong> <strong>-<\/strong><\/pre>\n<div class='ro' style='' lang='ro' dir='ltr'>\n<p>De aici rezult\u0103 c\u0103 exist\u0103 dou\u0103 solu\u021bii identice pentru valoarea cu\u021bitului, \u0219i anume:<\/p>\n<p><span style=\"color: #ffff00;\">Cu\u021bitul cost\u0103 4 Lei.<\/span><\/p>\n<\/div>\n<div class='en' style='display:none;' lang='en' dir='ltr'>\n<p>From here we can see that there are two identical solutions for the value of the knife:<\/p>\n<p><span style=\"color: #ffff00;\">The knife costs 4 pounds.<\/span><\/p>\n<\/div>\n<div class='fr' style='display:none;' lang='fr' dir='ltr'>\n<p>D&#8217;ici on voit qu&#8217;il y a deux solutions identiques pour la valeur du couteau:<\/p>\n<p><span style=\"color: #ffff00;\">Le couteau coute 4 francs.<\/span><\/p>\n<\/div>\n\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Preambul Orice persoan\u0103 are nevoie \u00een via\u021b\u0103 de un pol fix, de un punct de sprijin \u00een care s\u0103 se \u00eencread\u0103 \u00een mod absolut, \u00een orice moment \u0219i \u00een orice condi\u021bii. Unii oameni fac apel la religie, al\u021bii fac apel la alte persoane de care sunt dependente, al\u021bii cred \u00een Steaua Polar\u0103 sau doar \u00een <a href='http:\/\/blog.copcea.ro\/?p=169' class='excerpt-more'>[&#8230;]<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,15],"tags":[127,129,128,132,131,130],"_links":{"self":[{"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=\/wp\/v2\/posts\/169"}],"collection":[{"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=169"}],"version-history":[{"count":48,"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=\/wp\/v2\/posts\/169\/revisions"}],"predecessor-version":[{"id":1683,"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=\/wp\/v2\/posts\/169\/revisions\/1683"}],"wp:attachment":[{"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=169"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.copcea.ro\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}