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受欢迎的代数 >

x^6+4x^3-1=0

解答

x^{6} + 4 x^{3} - 1 = 0

解答

x = 3 - 2 + 5, x = - 3 - 2 + 5 \frac{1}{2} + 3 - 2 + 5 \frac{3}{2} i, x = - 3 - 2 + 5 \frac{1}{2} - 3 - 2 + 5 \frac{3}{2} i, x = 3 - 2 - 5, x = - 3 - 2 - 5 \frac{1}{2} + 3 - 2 - 5 \frac{3}{2} i, x = - 3 - 2 - 5 \frac{1}{2} - 3 - 2 - 5 \frac{3}{2} i

求解步骤

x^{6} + 4 x^{3} - 1 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

u^{2} + 4 u - 1 = 0

解

u^{2} + 4 u - 1 = 0 : u = - 2 + 5, u = - 2 - 5

u = - 2 + 5, u = - 2 - 5

代回

u = x^{3}

，求解

x

解

x^{3} = - 2 + 5 : x = 3 - 2 + 5, x = - 3 - 2 + 5 \frac{1}{2} + 3 - 2 + 5 \frac{3}{2} i, x = - 3 - 2 + 5 \frac{1}{2} - 3 - 2 + 5 \frac{3}{2} i

解

x^{3} = - 2 - 5 : x = 3 - 2 - 5, x = - 3 - 2 - 5 \frac{1}{2} + 3 - 2 - 5 \frac{3}{2} i, x = - 3 - 2 - 5 \frac{1}{2} - 3 - 2 - 5 \frac{3}{2} i

解为

x = 3 - 2 + 5, x = - 3 - 2 + 5 \frac{1}{2} + 3 - 2 + 5 \frac{3}{2} i, x = - 3 - 2 + 5 \frac{1}{2} - 3 - 2 + 5 \frac{3}{2} i, x = 3 - 2 - 5, x = - 3 - 2 - 5 \frac{1}{2} + 3 - 2 - 5 \frac{3}{2} i, x = - 3 - 2 - 5 \frac{1}{2} - 3 - 2 - 5 \frac{3}{2} i

作图

流行的例子

solvefor x,x^4+3x^2-4=0

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

a^{4} - 1 = 0

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(x^2-x)^2-5(x^2-x)+6=0

(x^{2} - x)^{2} - 5 (x^{2} - x) + 6 = 0

6x^4-x^3-26x+4x+8=0

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