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受欢迎的代数 >

z^6-z^3-2=0

解答

z^{6} - z^{3} - 2 = 0

解答

z = 32, z = - 32 \frac{1}{2} + 32 \frac{3}{2} i, z = - 32 \frac{1}{2} - 32 \frac{3}{2} i, z = - 1, z = \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} + \frac{3}{2} i

求解步骤

z^{6} - z^{3} - 2 = 0

用

u = z^{3}

和

u^{2} = z^{6}

改写方程式

u^{2} - u - 2 = 0

解

u^{2} - u - 2 = 0 : u = 2, u = - 1

u = 2, u = - 1

代回

u = z^{3}

，求解

z

解

z^{3} = 2 : z = 32, z = - 32 \frac{1}{2} + 32 \frac{3}{2} i, z = - 32 \frac{1}{2} - 32 \frac{3}{2} i

解

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

解为

z = 32, z = - 32 \frac{1}{2} + 32 \frac{3}{2} i, z = - 32 \frac{1}{2} - 32 \frac{3}{2} i, z = - 1, z = \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} + \frac{3}{2} i

作图

流行的例子

x^3-9x^2-25x+33=0

x^{3} - 9 x^{2} - 25 x + 33 = 0

m^{3} + 4 m = 0

r^4+r^3-7r^2-r+6=0

r^{4} + r^{3} - 7 r^{2} - r + 6 = 0

4 x - 4 x^{9} = 0

solvefor y,(x^2+y^2)^2=x^2-y^2

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