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受欢迎的代数 >

(x+1)(x^2-x+1)=(x-1)^3

解答

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

解答

x = \frac{1}{2} - i \frac{15}{6}, x = \frac{1}{2} + i \frac{15}{6}

求解步骤

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

展开

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

展开

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

x^{3} + 1 = x^{3} - 3 x^{2} + 3 x - 1

交换两边

x^{3} - 3 x^{2} + 3 x - 1 = x^{3} + 1

将

1

para o lado esquerdo

x^{3} - 3 x^{2} + 3 x - 2 = x^{3}

将

x^{3}

para o lado esquerdo

- 3 x^{2} + 3 x - 2 = 0

使用求根公式求解

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

化简

3^{2} - 4 (- 3) (- 2) : 15 i

x_{1, 2} = \frac{- 3 \pm 15 i}{2 ( - 3 )}

将解分隔开

x_{1} = \frac{- 3 + 15 i}{2 ( - 3 )}, x_{2} = \frac{- 3 - 15 i}{2 ( - 3 )}

x = \frac{- 3 + 15 i}{2 ( - 3 )} : \frac{1}{2} - i \frac{15}{6}

x = \frac{- 3 - 15 i}{2 ( - 3 )} : \frac{1}{2} + i \frac{15}{6}

二次方程组的解是:

x = \frac{1}{2} - i \frac{15}{6}, x = \frac{1}{2} + i \frac{15}{6}

作图

流行的例子

solvefor x,g(x+2)=x^2-10x-3

so l v e f or x, g (x + 2) = x^{2} - 10 x - 3

x (2 x - 9) = 0

3 y^{2} + 7 y + 10 = 3

因式分解 2t^2+5=7t

f a c t or 2 t^{2} + 5 = 7 t

x^{2} + 6 x - 35 = 0