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受欢迎的代数 >

(2x-2)^2=-2(x-3/4)^2+9/8

解答

(2 x - 2)^{2} = - 2 (x - \frac{3}{4})^{2} + \frac{9}{8}

解答

x = \frac{4}{3}, x = \frac{1}{2}

+1

十进制

x = 1.33333 \dots, x = 0.5

求解步骤

(2 x - 2)^{2} = - 2 (x - \frac{3}{4})^{2} + \frac{9}{8}

在两边乘以

8

8 (2 x - 2)^{2} = - 16 (x - \frac{3}{4})^{2} + 9

展开

8 (2 x - 2)^{2} : 32 x^{2} - 64 x + 32

展开

- 16 (x - \frac{3}{4})^{2} + 9 : - 16 x^{2} + 24 x

32 x^{2} - 64 x + 32 = - 16 x^{2} + 24 x

将

24 x

para o lado esquerdo

32 x^{2} - 88 x + 32 = - 16 x^{2}

将

16 x^{2}

para o lado esquerdo

48 x^{2} - 88 x + 32 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 88 ) \pm ( - 88 ) ^{2} - 4 \cdot 48 \cdot 32}{2 \cdot 48}

(- 88)^{2} - 4 \cdot 48 \cdot 32 = 40

x_{1, 2} = \frac{- ( - 88 ) \pm 40}{2 \cdot 48}

将解分隔开

x_{1} = \frac{- ( - 88 ) + 40}{2 \cdot 48}, x_{2} = \frac{- ( - 88 ) - 40}{2 \cdot 48}

x = \frac{- ( - 88 ) + 40}{2 \cdot 48} : \frac{4}{3}

x = \frac{- ( - 88 ) - 40}{2 \cdot 48} : \frac{1}{2}

二次方程组的解是:

x = \frac{4}{3}, x = \frac{1}{2}

作图

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