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受欢迎的代数 >

(x+1)(x-1)=2(x-13)^2

解答

(x + 1) (x - 1) = 2 (x - 13)^{2}

解答

x = 26 + 337, x = 26 - 337

+1

十进制

x = 44.35755 \dots, x = 7.64244 \dots

求解步骤

(x + 1) (x - 1) = 2 (x - 13)^{2}

展开

(x + 1) (x - 1) : x^{2} - 1

展开

2 (x - 13)^{2} : 2 x^{2} - 52 x + 338

x^{2} - 1 = 2 x^{2} - 52 x + 338

交换两边

2 x^{2} - 52 x + 338 = x^{2} - 1

将

1

para o lado esquerdo

2 x^{2} - 52 x + 339 = x^{2}

将

x^{2}

para o lado esquerdo

x^{2} - 52 x + 339 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 52 ) \pm ( - 52 ) ^{2} - 4 \cdot 1 \cdot 339}{2 \cdot 1}

(- 52)^{2} - 4 \cdot 1 \cdot 339 = 2337

x_{1, 2} = \frac{- ( - 52 ) \pm 2 337}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( - 52 ) + 2 337}{2 \cdot 1}, x_{2} = \frac{- ( - 52 ) - 2 337}{2 \cdot 1}

x = \frac{- ( - 52 ) + 2 337}{2 \cdot 1} : 26 + 337

x = \frac{- ( - 52 ) - 2 337}{2 \cdot 1} : 26 - 337

二次方程组的解是:

x = 26 + 337, x = 26 - 337

作图

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