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受欢迎的代数 >

solvefor x,(x+k)(x^2+3x-1)=x^3-x^2-13x+4

解答

x, (x + k) (x^{2} + 3 x - 1) = x^{3} - x^{2} - 13 x + 4

解答

x = \frac{- 3 + 13}{2}, x = - \frac{3 + 13}{2}; k \neq = - 4

+1

十进制

x = 0.30277 \dots, x = - 3.30277 \dots

求解步骤

(x + k) (x^{2} + 3 x - 1) = x^{3} - x^{2} - 13 x + 4

展开

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

x^{3} + 3 x^{2} - x + k x^{2} + 3 k x - k = x^{3} - x^{2} - 13 x + 4

两边减去

x^{3} - x^{2} - 13 x + 4

x^{3} + 3 x^{2} - x + k x^{2} + 3 k x - k - (x^{3} - x^{2} - 13 x + 4) = x^{3} - x^{2} - 13 x + 4 - (x^{3} - x^{2} - 13 x + 4)

化简

(k + 4) x^{2} + (3 k + 12) x - k - 4 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 3 k + 12 ) \pm ( 3 k + 12 ) ^{2} - 4 ( k + 4 ) ( - k - 4 )}{2 ( k + 4 )}

化简

(3 k + 12)^{2} - 4 (k + 4) (- k - 4) : 13 (k + 4)

x_{1, 2} = \frac{- ( 3 k + 12 ) \pm 13 ( k + 4 )}{2 ( k + 4 )}; k \neq = - 4

将解分隔开

x_{1} = \frac{- ( 3 k + 12 ) + 13 ( k + 4 )}{2 ( k + 4 )}, x_{2} = \frac{- ( 3 k + 12 ) - 13 ( k + 4 )}{2 ( k + 4 )}

x = \frac{- ( 3 k + 12 ) + 13 ( k + 4 )}{2 ( k + 4 )} : \frac{- 3 + 13}{2}

x = \frac{- ( 3 k + 12 ) - 13 ( k + 4 )}{2 ( k + 4 )} : - \frac{3 + 13}{2}

二次方程组的解是:

x = \frac{- 3 + 13}{2}, x = - \frac{3 + 13}{2}; k \neq = - 4

作图

流行的例子

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x^2-2/3 x+1/12 =0

x^{2} - \frac{2}{3} x + \frac{1}{12} = 0

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12 x^{2} + 57 x + 45 = 0

(x + 5)^{2} = 5