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受欢迎的代数 >

3x^4-15x^2=23

解答

3 x^{4} - 15 x^{2} = 23

解答

x = \frac{15 + 501}{6}, x = - \frac{15 + 501}{6}, x = \frac{15 - 501}{6}, x = - \frac{15 - 501}{6}

求解步骤

3 x^{4} - 15 x^{2} = 23

将

23

para o lado esquerdo

3 x^{4} - 15 x^{2} - 23 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

3 u^{2} - 15 u - 23 = 0

解

3 u^{2} - 15 u - 23 = 0 : u = \frac{15 + 501}{6}, u = \frac{15 - 501}{6}

u = \frac{15 + 501}{6}, u = \frac{15 - 501}{6}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{15 + 501}{6} : x = \frac{15 + 501}{6}, x = - \frac{15 + 501}{6}

解

x^{2} = \frac{15 - 501}{6} : x = \frac{15 - 501}{6}, x = - \frac{15 - 501}{6}

解为

x = \frac{15 + 501}{6}, x = - \frac{15 + 501}{6}, x = \frac{15 - 501}{6}, x = - \frac{15 - 501}{6}

作图

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