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受欢迎的代数 >

(x+13)^2=(x+12)^2+(x-5)^2

解答

(x + 13)^{2} = (x + 12)^{2} + (x - 5)^{2}

解答

x = 0, x = 12

求解步骤

(x + 13)^{2} = (x + 12)^{2} + (x - 5)^{2}

展开

(x + 13)^{2} : x^{2} + 26 x + 169

展开

(x + 12)^{2} + (x - 5)^{2} : 2 x^{2} + 14 x + 169

x^{2} + 26 x + 169 = 2 x^{2} + 14 x + 169

将

169

para o lado esquerdo

x^{2} + 26 x = 2 x^{2} + 14 x

将

14 x

para o lado esquerdo

x^{2} + 12 x = 2 x^{2}

将

2 x^{2}

para o lado esquerdo

- x^{2} + 12 x = 0

使用求根公式求解

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 ( - 1 ) \cdot 0}{2 ( - 1 )}

1 2^{2} - 4 (- 1) \cdot 0 = 12

x_{1, 2} = \frac{- 12 \pm 12}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- 12 + 12}{2 ( - 1 )}, x_{2} = \frac{- 12 - 12}{2 ( - 1 )}

x = \frac{- 12 + 12}{2 ( - 1 )} : 0

x = \frac{- 12 - 12}{2 ( - 1 )} : 12

二次方程组的解是:

x = 0, x = 12

作图

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