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受欢迎的代数 >

3(x^2+1)=x(x-3)

解答

3 (x^{2} + 1) = x (x - 3)

解答

x = - \frac{3}{4} + i \frac{15}{4}, x = - \frac{3}{4} - i \frac{15}{4}

求解步骤

3 (x^{2} + 1) = x (x - 3)

展开

3 (x^{2} + 1) : 3 x^{2} + 3

展开

x (x - 3) : x^{2} - 3 x

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

将

3 x

para o lado esquerdo

3 x^{2} + 3 + 3 x = x^{2}

将

x^{2}

para o lado esquerdo

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

使用求根公式求解

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

化简

3^{2} - 4 \cdot 2 \cdot 3 : 15 i

x_{1, 2} = \frac{- 3 \pm 15 i}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- 3 + 15 i}{2 \cdot 2}, x_{2} = \frac{- 3 - 15 i}{2 \cdot 2}

x = \frac{- 3 + 15 i}{2 \cdot 2} : - \frac{3}{4} + i \frac{15}{4}

x = \frac{- 3 - 15 i}{2 \cdot 2} : - \frac{3}{4} - i \frac{15}{4}

二次方程组的解是:

x = - \frac{3}{4} + i \frac{15}{4}, x = - \frac{3}{4} - i \frac{15}{4}

作图

流行的例子

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