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受欢迎的代数 >

ax^2+2a=x+2a^2x

解答

a x^{2} + 2 a = x + 2 a^{2} x

解答

x = 2 a, x = \frac{1}{a}; a \neq = 0

求解步骤

a x^{2} + 2 a = x + 2 a^{2} x

将

2 a^{2} x

para o lado esquerdo

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

将

x

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(- 2 a^{2} - 1)^{2} - 4 a \cdot 2 a : (2 a + 1) (2 a - 1)

x_{1, 2} = \frac{- ( - 2 a ^{2} - 1 ) \pm ( 2 a + 1 ) ( 2 a - 1 )}{2 a}; a \neq = 0

将解分隔开

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

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

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

二次方程组的解是:

x = 2 a, x = \frac{1}{a}; a \neq = 0

作图

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