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受欢迎的代数 >

ax^2+bx+7=k(3x^2-2x+1)

解答

a x^{2} + b x + 7 = k (3 x^{2} - 2 x + 1)

解答

x = \frac{- b - 2 k + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}, x = \frac{- b - 2 k - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}; k \neq = \frac{a}{3}

求解步骤

a x^{2} + b x + 7 = k (3 x^{2} - 2 x + 1)

展开

k (3 x^{2} - 2 x + 1) : 3 k x^{2} - 2 k x + k

a x^{2} + b x + 7 = 3 k x^{2} - 2 k x + k

两边减去

- 2 k x + k

a x^{2} + b x + 7 - (- 2 k x + k) = 3 k x^{2} - 2 k x + k - (- 2 k x + k)

化简

a x^{2} + b x + 7 + 2 k x - k = 3 k x^{2}

将

3 k x^{2}

para o lado esquerdo

a x^{2} + b x + 7 + 2 k x - k - 3 k x^{2} = 0

改写成标准形式

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

(a - 3 k) x^{2} + (b + 2 k) x + 7 - k = 0

使用求根公式求解

x_{1, 2} = \frac{- ( b + 2 k ) \pm ( b + 2 k ) ^{2} - 4 ( a - 3 k ) ( 7 - k )}{2 ( a - 3 k )}

化简

(b + 2 k)^{2} - 4 (a - 3 k) (7 - k) : - 8 k^{2} + 4 ak + 4 bk + 84 k - 28 a + b^{2}

x_{1, 2} = \frac{- ( b + 2 k ) \pm - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}; k \neq = \frac{a}{3}

将解分隔开

x_{1} = \frac{- ( b + 2 k ) + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}, x_{2} = \frac{- ( b + 2 k ) - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}

x = \frac{- ( b + 2 k ) + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )} : \frac{- b - 2 k + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}

x = \frac{- ( b + 2 k ) - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )} : \frac{- b - 2 k - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}

二次方程组的解是:

x = \frac{- b - 2 k + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}, x = \frac{- b - 2 k - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}; k \neq = \frac{a}{3}

作图

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