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受欢迎的代数 >

a^8=3

解答

a^{8} = 3

解答

a = 43, a = - 43, a = 43 i, a = - 43 i, a = \frac{4 3}{2} + \frac{8 3}{2} i, a = - \frac{4 3}{2} - \frac{8 3}{2} i, a = \frac{4 3}{2} - \frac{8 3}{2} i, a = - \frac{4 3}{2} + \frac{8 3}{2} i

求解步骤

a^{8} = 3

用

u = a^{2}

和

u^{4} = a^{8}

改写方程式

u^{4} = 3

解

u^{4} = 3 : u = 3, u = - 3, u = 3 i, u = - 3 i

u = 3, u = - 3, u = 3 i, u = - 3 i

代回

u = a^{2}

，求解

a

解

a^{2} = 3 : a = 43, a = - 43

解

a^{2} = - 3 : a = 43 i, a = - 43 i

解

a^{2} = 3 i : a = \frac{4 3}{2} + \frac{8 3}{2} i, a = - \frac{4 3}{2} - \frac{8 3}{2} i

解

a^{2} = - 3 i : a = \frac{4 3}{2} - \frac{8 3}{2} i, a = - \frac{4 3}{2} + \frac{8 3}{2} i

解为

a = 43, a = - 43, a = 43 i, a = - 43 i, a = \frac{4 3}{2} + \frac{8 3}{2} i, a = - \frac{4 3}{2} - \frac{8 3}{2} i, a = \frac{4 3}{2} - \frac{8 3}{2} i, a = - \frac{4 3}{2} + \frac{8 3}{2} i

作图

流行的例子

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

solvefor x,0=-25x^4+9x^2

so l v e f or x, 0 = - 25 x^{4} + 9 x^{2}

solvefor x,y+x^3=2

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

2 x^{5} + 64 = 0

(x + 6)^{3} + 27 = 0