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受欢迎的代数 >

(x-4)^3=x(x^2+2x)

解答

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

解答

x = \frac{12}{7} - i \frac{4 5}{7}, x = \frac{12}{7} + i \frac{4 5}{7}

求解步骤

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

展开

(x - 4)^{3} : x^{3} - 12 x^{2} + 48 x - 64

展开

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

x^{3} - 12 x^{2} + 48 x - 64 = x^{3} + 2 x^{2}

将

2 x^{2}

para o lado esquerdo

x^{3} - 14 x^{2} + 48 x - 64 = x^{3}

将

x^{3}

para o lado esquerdo

- 14 x^{2} + 48 x - 64 = 0

使用求根公式求解

x_{1, 2} = \frac{- 48 \pm 4 8 ^{2} - 4 ( - 14 ) ( - 64 )}{2 ( - 14 )}

化简

4 8^{2} - 4 (- 14) (- 64) : 165 i

x_{1, 2} = \frac{- 48 \pm 16 5 i}{2 ( - 14 )}

将解分隔开

x_{1} = \frac{- 48 + 16 5 i}{2 ( - 14 )}, x_{2} = \frac{- 48 - 16 5 i}{2 ( - 14 )}

x = \frac{- 48 + 16 5 i}{2 ( - 14 )} : \frac{12}{7} - i \frac{4 5}{7}

x = \frac{- 48 - 16 5 i}{2 ( - 14 )} : \frac{12}{7} + i \frac{4 5}{7}

二次方程组的解是:

x = \frac{12}{7} - i \frac{4 5}{7}, x = \frac{12}{7} + i \frac{4 5}{7}

作图

流行的例子

solvefor x, r/f (x)=2x^2-2x-12

so l v e f or x, \frac{r}{f} (x) = 2 x^{2} - 2 x - 12

a(x^2+1)=x(a^2+1)

a (x^{2} + 1) = x (a^{2} + 1)

solvefor x,f(x^2+y^2+z^2z^2-2xy)=0

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

3 = xx + xx + xx

solvefor x,3x+4y(3x^2+4y^2)=0

so l v e f or x, 3 x + 4 y (3 x^{2} + 4 y^{2}) = 0