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受欢迎的代数 >

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

解答

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

解答

x = \frac{2}{3} + i \frac{2}{3}, x = \frac{2}{3} - i \frac{2}{3}

求解步骤

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

展开

4 (x^{2} - x) : 4 x^{2} - 4 x

4 x^{2} - 4 x = x^{2} - 2

将

2

para o lado esquerdo

4 x^{2} - 4 x + 2 = x^{2}

将

x^{2}

para o lado esquerdo

3 x^{2} - 4 x + 2 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 3 \cdot 2}{2 \cdot 3}

化简

(- 4)^{2} - 4 \cdot 3 \cdot 2 : 22 i

x_{1, 2} = \frac{- ( - 4 ) \pm 2 2 i}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- ( - 4 ) + 2 2 i}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2 2 i}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2 2 i}{2 \cdot 3} : \frac{2}{3} + i \frac{2}{3}

x = \frac{- ( - 4 ) - 2 2 i}{2 \cdot 3} : \frac{2}{3} - i \frac{2}{3}

二次方程组的解是:

x = \frac{2}{3} + i \frac{2}{3}, x = \frac{2}{3} - i \frac{2}{3}

作图

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