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受欢迎的代数 >

(a-b)x^2+(c-a)x+(b-c)=0

解答

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

解答

x = \frac{- c + a + a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}, x = \frac{- c + a - a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}; a - b \neq = 0

求解步骤

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

展开

(a - b) x^{2} + (c - a) x + (b - c) : a x^{2} - b x^{2} + c x - a x + b - c

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(c - a)^{2} - 4 (a - b) (b - c) : a^{2} - 4 ab + 2 a c + 4 b^{2} + c^{2} - 4 b c

x_{1, 2} = \frac{- ( c - a ) \pm a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}; a - b \neq = 0

将解分隔开

x_{1} = \frac{- ( c - a ) + a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}, x_{2} = \frac{- ( c - a ) - a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}

x = \frac{- ( c - a ) + a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )} : \frac{- c + a + a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}

x = \frac{- ( c - a ) - a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )} : \frac{- c + a - a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}

二次方程组的解是:

x = \frac{- c + a + a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}, x = \frac{- c + a - a ^{2} - 4 ab + 2 a c + 4 b ^{2} + c ^{2} - 4 b c}{2 ( a - b )}; a - b \neq = 0

作图

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