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受欢迎的代数 >

x^4+2x^2+5=0

解答

x^{4} + 2 x^{2} + 5 = 0

解答

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

求解步骤

x^{4} + 2 x^{2} + 5 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} + 2 u + 5 = 0

解

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

u = - 1 + 2 i, u = - 1 - 2 i

代回

u = x^{2}

，求解

x

解

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

解

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

解为

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

作图

流行的例子

solvefor y,y^6=x

so l v e f or y, y^{6} = x

t^{5} = 9 t^{3}

z^{8} = 256

m^{4} + m^{2} + 1 = 0

solvefor a,a^3-b^3=0

so l v e f or a, a^{3} - b^{3} = 0