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受欢迎的代数 >

x^2+2/3 ax+(-(a^2)/2+1)=0

解答

x^{2} + \frac{2}{3} a x + (- \frac{a ^{2}}{2} + 1) = 0

解答

x = \frac{- a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}, x = - \frac{a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

求解步骤

x^{2} + \frac{2}{3} a x + (- \frac{a ^{2}}{2} + 1) = 0

在两边乘以

3

3 x^{2} + 2 a x + 3 (- \frac{a ^{2}}{2} + 1) = 0

展开

3 x^{2} + 2 a x + 3 (- \frac{a ^{2}}{2} + 1) : 3 x^{2} + 2 a x - \frac{3 a ^{2}}{2} + 3

3 x^{2} + 2 a x - \frac{3 a ^{2}}{2} + 3 = 0

使用求根公式求解

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

化简

(2 a)^{2} - 4 \cdot 3 (- \frac{3 a ^{2}}{2} + 3) : 2 a^{2} - 3 (3 - \frac{3 a ^{2}}{2})

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

将解分隔开

x_{1} = \frac{- 2 a + 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3}, x_{2} = \frac{- 2 a - 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3}

x = \frac{- 2 a + 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3} : \frac{- a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

x = \frac{- 2 a - 2 a ^{2} - 3 ( 3 - \frac{3 a ^{2}}{2} )}{2 \cdot 3} : - \frac{a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

二次方程组的解是:

x = \frac{- a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}, x = - \frac{a + a ^{2} - 3 ( - \frac{3 a ^{2}}{2} + 3 )}{3}

作图

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