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受欢迎的代数 >

(x+a)^2-(x+a)-12=0

解答

(x + a)^{2} - (x + a) - 12 = 0

解答

x = - a + 4, x = - a - 3

求解步骤

(x + a)^{2} - (x + a) - 12 = 0

展开

(x + a)^{2} - (x + a) - 12 : x^{2} + 2 a x + a^{2} - x - a - 12

x^{2} + 2 a x + a^{2} - x - a - 12 = 0

改写成标准形式

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

x^{2} + (2 a - 1) x + a^{2} - a - 12 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 2 a - 1 ) \pm ( 2 a - 1 ) ^{2} - 4 \cdot 1 \cdot ( a ^{2} - a - 12 )}{2 \cdot 1}

(2 a - 1)^{2} - 4 \cdot 1 \cdot (a^{2} - a - 12) = 7

x_{1, 2} = \frac{- ( 2 a - 1 ) \pm 7}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( 2 a - 1 ) + 7}{2 \cdot 1}, x_{2} = \frac{- ( 2 a - 1 ) - 7}{2 \cdot 1}

x = \frac{- ( 2 a - 1 ) + 7}{2 \cdot 1} : - a + 4

x = \frac{- ( 2 a - 1 ) - 7}{2 \cdot 1} : - a - 3

二次方程组的解是:

x = - a + 4, x = - a - 3

作图

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