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受欢迎的代数 >

(x-3)^2+(x+4)^2-(x-5)^2=17x+24

解答

(x - 3)^{2} + (x + 4)^{2} - (x - 5)^{2} = 17 x + 24

解答

x = 8, x = - 3

求解步骤

(x - 3)^{2} + (x + 4)^{2} - (x - 5)^{2} = 17 x + 24

展开

(x - 3)^{2} + (x + 4)^{2} - (x - 5)^{2} : x^{2} + 12 x

x^{2} + 12 x = 17 x + 24

将

24

para o lado esquerdo

x^{2} + 12 x - 24 = 17 x

将

17 x

para o lado esquerdo

x^{2} - 5 x - 24 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot ( - 24 )}{2 \cdot 1}

(- 5)^{2} - 4 \cdot 1 \cdot (- 24) = 11

x_{1, 2} = \frac{- ( - 5 ) \pm 11}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( - 5 ) + 11}{2 \cdot 1}, x_{2} = \frac{- ( - 5 ) - 11}{2 \cdot 1}

x = \frac{- ( - 5 ) + 11}{2 \cdot 1} : 8

x = \frac{- ( - 5 ) - 11}{2 \cdot 1} : - 3

二次方程组的解是:

x = 8, x = - 3

作图

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(x - 10)^{2} + 10 = 100

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