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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Equating coefficients ： ウィキペディア英語版 Equating coefficients In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term. The method is used to bring formulas into a desired form. ==Example in real fractions== Suppose we want to apply partial fraction decomposition to the expression: :$\backslash frac,\backslash ,$ that is, we want to bring it into the form: :$\backslash frac+\backslash frac+\backslash frac,\backslash ,$ in which the unknown parameters are ''A'', ''B'' and ''C''. Multiplying these formulas by ''x''(''x'' − 1)(''x'' − 2) turns both into polynomials, which we equate: :$A(x-1)(x-2)\; +\; Bx(x-2)\; +\; Cx(x-1)\; =\; 1,\backslash ,$ or, after expansion and collecting terms with equal powers of ''x'': :$(A+B+C)x^2\; -\; (3A+2B+C)x\; +\; 2A\; =\; 1.\backslash ,$ At this point it is essential to realize that the polynomial 1 is in fact equal to the polynomial 0''x''2 + 0''x'' + 1, having zero coefficients for the positive powers of ''x''. Equating the corresponding coefficients now results in this system of linear equations: :$A+B+C\; =\; 0,\backslash ,$ :$3A+2B+C\; =\; 0,\backslash ,$ :$2A\; =\; 1.\backslash ,$ Solving it results in: :$A\; =\; \backslash frac,\backslash ,\; B\; =\; -1,\backslash ,\; C\; =\; \backslash frac.\backslash ,$ 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「Equating coefficients」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.