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

解答

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

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

求解步骤

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

展开

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

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

改写成标准形式

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

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

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

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

二次方程组的解是:

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

so l v e f or a, 588 = a^{2} \cdot b

x^{2} - 1000 x - 30000 = 0

so l v e f or x, 12 x^{2} + 5 x y - 2 y^{2} = 0

so l v e f or a, \frac{b ^{2}}{c ^{2}} = \frac{1}{1} - \frac{a ^{2}}{c ^{2}}

so l v e f or x, p^{2} + x^{2} + (p^{2} - q^{2}) x - q^{2} = 0