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受欢迎的代数 >

x^6+12x^3+32=0

解答

x^{6} + 12 x^{3} + 32 = 0

解答

x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i, x = - 2, x = 1 - 3 i, x = 1 + 3 i

求解步骤

x^{6} + 12 x^{3} + 32 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

u^{2} + 12 u + 32 = 0

解

u^{2} + 12 u + 32 = 0 : u = - 4, u = - 8

u = - 4, u = - 8

代回

u = x^{3}

，求解

x

解

x^{3} = - 4 : x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i

解

x^{3} = - 8 : x = - 2, x = 1 - 3 i, x = 1 + 3 i

解为

x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i, x = - 2, x = 1 - 3 i, x = 1 + 3 i

作图

流行的例子

solvefor x,y^2=cx^4-2

so l v e f or x, y^{2} = c x^{4} - 2

x^{16} - 1 = 0

(x+3)(x^2+3x+5)=x^2+3x

(x + 3) (x^{2} + 3 x + 5) = x^{2} + 3 x

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

x^{3} + x^{2} - 36 = 0