翻訳と辞書 Words near each other ・ Bhaskar Pillai ・ Bhaskar Pramanik ・ Bhaskar Ramachandra Bhagwat ・ Bhaskar Ramamurthi ・ Bhaskar Ramchandra Tambe ・ Bhaskar Sadashiv Soman ・ Bhaskar Save ・ Bhaskar Sunkara ・ Bhaskar the Rascal ・ Bhaskar Tukaram Auti ・ Bhaskar Varman ・ Bhaskara (Kashmiri) ・ Bhaskara (satellite) ・ Bhaskara I's sine approximation formula ・ Bhaskara Sethupathi ・ Bhaskara's lemma ・ Bhaskaracharya Institute For Space Applications and Geo-Informatics ・ Bhaskaracharya Pratishthana ・ Bhaskaracharya Tripathi ・ Bhaskaran ・ Bhaskaran K. M. ・ Bhaskararajapuram ・ Bhaskararaya ・ Bhaskarathu ・ Bhaskarbuwa Bakhale ・ Bhaskareswarar Temple ・ Bhaskarrao Bapurao Khatgaonkar Patil ・ Bhaskar–Jagannathan syndrome ・ Bhasker Patel ・ Bhaskraycharya College of Applied Sciences Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bhaskara's lemma ： ウィキペディア英語版 Bhaskara's lemma ''Bhaskara's'' Lemma is an identity used as a lemma during the chakravala method. It states that: :$\backslash ,\; Nx^2\; +\; k\; =\; y^2\backslash implies\; \backslash ,N\backslash left(\backslash frac\backslash right)^2\; +\; \backslash frac\; =\; \backslash left(\backslash frac\backslash right)^2$ for integers $m,\backslash ,\; x,\backslash ,\; y,\backslash ,\; N,$ and non-zero integer $k$. ==Proof== The proof follows from simple algebraic manipulations as follows: multiply both sides of the equation by $m^2-N$, add $N^2x^2+2Nmxy+Ny^2$, factor, and divide by $k^2$. :$\backslash ,\; Nx^2\; +\; k\; =\; y^2\backslash implies\; Nm^2x^2-N^2x^2+k(m^2-N)\; =\; m^2y^2-Ny^2$ :$\backslash implies\; Nm^2x^2+2Nmxy+Ny^2+k(m^2-N)\; =\; m^2y^2+2Nmxy+N^2x^2$ :$\backslash implies\; N(mx+y)^2+k(m^2-N)\; =\; (my+Nx)^2$ :$\backslash implies\; \backslash ,N\backslash left(\backslash frac\backslash right)^2\; +\; \backslash frac\; =\; \backslash left(\backslash frac\backslash right)^2.$ So long as neither $k$ nor $m^2-N$ are zero, the implication goes in both directions. (Note also that the lemma holds for real or complex numbers as well as integers.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bhaskara's lemma」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.