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受欢迎的代数 >

8x^4+27=0

解答

8 x^{4} + 27 = 0

解答

x = \frac{4 27}{2 4 2} + \frac{3 ^{\frac{3}{4}}}{2 4 2} i, x = - \frac{4 27}{2 4 2} - \frac{3 ^{\frac{3}{4}}}{2 4 2} i, x = \frac{4 27}{2 4 2} - \frac{3 3}{2 ^{\frac{3}{4}} 2 4 27} i, x = - \frac{4 27}{2 4 2} + \frac{3 3}{2 ^{\frac{3}{4}} 2 4 27} i

求解步骤

8 x^{4} + 27 = 0

将

27

到右边

8 x^{4} = - 27

两边除以

8

x^{4} = - \frac{27}{8}

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} = - \frac{27}{8}

解

u^{2} = - \frac{27}{8} : u = \frac{3 3}{2 2} i, u = - \frac{3 3}{2 2} i

u = \frac{3 3}{2 2} i, u = - \frac{3 3}{2 2} i

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{3 3}{2 2} i : x = \frac{4 27}{2 4 2} + \frac{3 ^{\frac{3}{4}}}{2 4 2} i, x = - \frac{4 27}{2 4 2} - \frac{3 ^{\frac{3}{4}}}{2 4 2} i

解

x^{2} = - \frac{3 3}{2 2} i : x = \frac{4 27}{2 4 2} - \frac{3 3}{2 ^{\frac{3}{4}} 2 4 27} i, x = - \frac{4 27}{2 4 2} + \frac{3 3}{2 ^{\frac{3}{4}} 2 4 27} i

解为

x = \frac{4 27}{2 4 2} + \frac{3 ^{\frac{3}{4}}}{2 4 2} i, x = - \frac{4 27}{2 4 2} - \frac{3 ^{\frac{3}{4}}}{2 4 2} i, x = \frac{4 27}{2 4 2} - \frac{3 3}{2 ^{\frac{3}{4}} 2 4 27} i, x = - \frac{4 27}{2 4 2} + \frac{3 3}{2 ^{\frac{3}{4}} 2 4 27} i

作图

流行的例子

x^3+14x^2+76x+96=0

x^{3} + 14 x^{2} + 76 x + 96 = 0

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0 = x^{3} - 25 x

(x^2-3x+5)(x^2-3x+5)=9

(x^{2} - 3 x + 5) (x^{2} - 3 x + 5) = 9

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