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受欢迎的代数 >

x^6+x^4+x^2=16275

解答

x^{6} + x^{4} + x^{2} = 16275

解答

x = 5, x = - 5, x = \frac{- 13 + 651}{2} + \frac{651 + 13}{2} i, x = - \frac{- 13 + 651}{2} - \frac{651 + 13}{2} i, x = \frac{- 13 + 651}{2} - \frac{651 + 13}{2} i, x = - \frac{- 13 + 651}{2} + \frac{651 + 13}{2} i

求解步骤

x^{6} + x^{4} + x^{2} = 16275

将

16275

para o lado esquerdo

x^{6} + x^{4} + x^{2} - 16275 = 0

用

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

和

u^{3} = x^{6}

改写方程式

u^{3} + u^{2} + u - 16275 = 0

解

u^{3} + u^{2} + u - 16275 = 0 : u = 25, u = - 13 + 482 i, u = - 13 - 482 i

u = 25, u = - 13 + 482 i, u = - 13 - 482 i

代回

u = x^{2}

，求解

x

解

x^{2} = 25 : x = 5, x = - 5

解

x^{2} = - 13 + 482 i : x = \frac{- 13 + 651}{2} + \frac{651 + 13}{2} i, x = - \frac{- 13 + 651}{2} - \frac{651 + 13}{2} i

解

x^{2} = - 13 - 482 i : x = \frac{- 13 + 651}{2} - \frac{651 + 13}{2} i, x = - \frac{- 13 + 651}{2} + \frac{651 + 13}{2} i

解为

x = 5, x = - 5, x = \frac{- 13 + 651}{2} + \frac{651 + 13}{2} i, x = - \frac{- 13 + 651}{2} - \frac{651 + 13}{2} i, x = \frac{- 13 + 651}{2} - \frac{651 + 13}{2} i, x = - \frac{- 13 + 651}{2} + \frac{651 + 13}{2} i

作图

流行的例子

x^4+2x^3+x^2+2x+1=0

x^{4} + 2 x^{3} + x^{2} + 2 x + 1 = 0

x^4-5x^3+8x^2-5x+8=0

x^{4} - 5 x^{3} + 8 x^{2} - 5 x + 8 = 0

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