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受欢迎的代数 >

(5k+7)x^2+5(k+2)x+3k+5=0

解答

(5 k + 7) x^{2} + 5 (k + 2) x + 3 k + 5 = 0

解答

x = \frac{- 5 k - 10 + - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}, x = \frac{- 5 k - 10 - - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}; k \neq = - \frac{7}{5}

求解步骤

(5 k + 7) x^{2} + 5 (k + 2) x + 3 k + 5 = 0

展开

(5 k + 7) x^{2} + 5 (k + 2) x + 3 k + 5 : 5 k x^{2} + 7 x^{2} + 5 k x + 10 x + 3 k + 5

5 k x^{2} + 7 x^{2} + 5 k x + 10 x + 3 k + 5 = 0

改写成标准形式

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

(5 k + 7) x^{2} + (5 k + 10) x + 3 k + 5 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 5 k + 10 ) \pm ( 5 k + 10 ) ^{2} - 4 ( 5 k + 7 ) ( 3 k + 5 )}{2 ( 5 k + 7 )}

化简

(5 k + 10)^{2} - 4 (5 k + 7) (3 k + 5) : - 35 k^{2} - 84 k - 40

x_{1, 2} = \frac{- ( 5 k + 10 ) \pm - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}; k \neq = - \frac{7}{5}

将解分隔开

x_{1} = \frac{- ( 5 k + 10 ) + - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}, x_{2} = \frac{- ( 5 k + 10 ) - - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}

x = \frac{- ( 5 k + 10 ) + - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )} : \frac{- 5 k - 10 + - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}

x = \frac{- ( 5 k + 10 ) - - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )} : \frac{- 5 k - 10 - - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}

二次方程组的解是:

x = \frac{- 5 k - 10 + - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}, x = \frac{- 5 k - 10 - - 35 k ^{2} - 84 k - 40}{2 ( 5 k + 7 )}; k \neq = - \frac{7}{5}

作图

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