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受欢迎的代数 >

x^8+24x^4=25

解答

x^{8} + 24 x^{4} = 25

解答

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

求解步骤

x^{8} + 24 x^{4} = 25

将

25

para o lado esquerdo

x^{8} + 24 x^{4} - 25 = 0

用

u = x^{2}, u^{2} = x^{4}

和

u^{4} = x^{8}

改写方程式

u^{4} + 24 u^{2} - 25 = 0

解

u^{4} + 24 u^{2} - 25 = 0 : u = 1, u = - 1, u = 5 i, u = - 5 i

u = 1, u = - 1, u = 5 i, u = - 5 i

代回

u = x^{2}

，求解

x

解

x^{2} = 1 : x = 1, x = - 1

解

x^{2} = - 1 : x = i, x = - i

解

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

解

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

解为

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

作图

流行的例子

(1 + x)^{9} = 2

a^{3} = 3

solvefor y,x+y^3=27

so l v e f or y, x + y^{3} = 27

(x^2+3)^2+7x^2+21=-10

(x^{2} + 3)^{2} + 7 x^{2} + 21 = - 10

5 y (y - 4) (y - 7) = 0