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受欢迎的代数 >

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

解答

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

解答

x = \frac{- 5 + 4 2}{2 2} + \frac{7}{2 2 - 5 + 4 2} i, x = - \frac{- 5 + 4 2}{2 2} - \frac{7}{2 2 - 5 + 4 2} i, x = \frac{- 5 + 4 2}{2 2} - \frac{7}{2 2 - 5 + 4 2} i, x = - \frac{- 5 + 4 2}{2 2} + \frac{7}{2 2 - 5 + 4 2} i

求解步骤

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

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

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

解

2 u^{2} + 5 u + 4 = 0 : u = - \frac{5}{4} + i \frac{7}{4}, u = - \frac{5}{4} - i \frac{7}{4}

u = - \frac{5}{4} + i \frac{7}{4}, u = - \frac{5}{4} - i \frac{7}{4}

代回

u = x^{2}

，求解

x

解

x^{2} = - \frac{5}{4} + i \frac{7}{4} : x = \frac{- 5 + 4 2}{2 2} + \frac{7}{2 2 - 5 + 4 2} i, x = - \frac{- 5 + 4 2}{2 2} - \frac{7}{2 2 - 5 + 4 2} i

解

x^{2} = - \frac{5}{4} - i \frac{7}{4} : x = \frac{- 5 + 4 2}{2 2} - \frac{7}{2 2 - 5 + 4 2} i, x = - \frac{- 5 + 4 2}{2 2} + \frac{7}{2 2 - 5 + 4 2} i

解为

x = \frac{- 5 + 4 2}{2 2} + \frac{7}{2 2 - 5 + 4 2} i, x = - \frac{- 5 + 4 2}{2 2} - \frac{7}{2 2 - 5 + 4 2} i, x = \frac{- 5 + 4 2}{2 2} - \frac{7}{2 2 - 5 + 4 2} i, x = - \frac{- 5 + 4 2}{2 2} + \frac{7}{2 2 - 5 + 4 2} i

作图

流行的例子

y^{4} + 15 y^{2} - 16 = 0

(2x-b)(4x^2-8x+3)=0

(2 x - b) (4 x^{2} - 8 x + 3) = 0

-x^3-3x^2-3x-1=0

- x^{3} - 3 x^{2} - 3 x - 1 = 0

x^{6} - x^{2} = 0

solvefor x,x^3-64=0

so l v e f or x, x^{3} - 64 = 0