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受欢迎的代数 >

5x^4+3x^2=0

解答

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

解答

x = 0, x = \frac{3}{5} i, x = - \frac{3}{5} i

求解步骤

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

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

5 u^{2} + 3 u = 0

解

5 u^{2} + 3 u = 0 : u = 0, u = - \frac{3}{5}

u = 0, u = - \frac{3}{5}

代回

u = x^{2}

，求解

x

解

x^{2} = 0 : x = 0

解

x^{2} = - \frac{3}{5} : x = \frac{3}{5} i, x = - \frac{3}{5} i

解为

x = 0, x = \frac{3}{5} i, x = - \frac{3}{5} i

作图

流行的例子

9x^6+6x^4-10000=0

9 x^{6} + 6 x^{4} - 10000 = 0

(x^{2} - 5) (x - 2) = 0

12x^3+27x^2-30x=0

12 x^{3} + 27 x^{2} - 30 x = 0

(1 - x^{2})^{2} = 0

x^{3} = - 343