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受欢迎的代数 >

4(10-x)^2=5x^2

解答

4 (10 - x)^{2} = 5 x^{2}

解答

x = - 20 (2 + 5), x = 20 (5 - 2)

+1

十进制

x = - 84.72135 \dots, x = 4.72135 \dots

求解步骤

4 (10 - x)^{2} = 5 x^{2}

展开

4 (10 - x)^{2} : 400 - 80 x + 4 x^{2}

400 - 80 x + 4 x^{2} = 5 x^{2}

将

5 x^{2}

para o lado esquerdo

400 - 80 x - x^{2} = 0

改写成标准形式

a x^{2} + b x + c = 0

- x^{2} - 80 x + 400 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 80 ) \pm ( - 80 ) ^{2} - 4 ( - 1 ) \cdot 400}{2 ( - 1 )}

(- 80)^{2} - 4 (- 1) \cdot 400 = 405

x_{1, 2} = \frac{- ( - 80 ) \pm 40 5}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- ( - 80 ) + 40 5}{2 ( - 1 )}, x_{2} = \frac{- ( - 80 ) - 40 5}{2 ( - 1 )}

x = \frac{- ( - 80 ) + 40 5}{2 ( - 1 )} : - 20 (2 + 5)

x = \frac{- ( - 80 ) - 40 5}{2 ( - 1 )} : 20 (5 - 2)

二次方程组的解是:

x = - 20 (2 + 5), x = 20 (5 - 2)

作图

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