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受欢迎的代数 >

2x^6+7x^3-15=0

解答

2 x^{6} + 7 x^{3} - 15 = 0

解答

x = 3 \frac{3}{2}, x = - 3 \frac{3}{2} \frac{1}{2} + 3 \frac{3}{2} \frac{3}{2} i, x = - 3 \frac{3}{2} \frac{1}{2} - 3 \frac{3}{2} \frac{3}{2} i, x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

求解步骤

2 x^{6} + 7 x^{3} - 15 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

2 u^{2} + 7 u - 15 = 0

解

2 u^{2} + 7 u - 15 = 0 : u = \frac{3}{2}, u = - 5

u = \frac{3}{2}, u = - 5

代回

u = x^{3}

，求解

x

解

x^{3} = \frac{3}{2} : x = 3 \frac{3}{2}, x = - 3 \frac{3}{2} \frac{1}{2} + 3 \frac{3}{2} \frac{3}{2} i, x = - 3 \frac{3}{2} \frac{1}{2} - 3 \frac{3}{2} \frac{3}{2} i

解

x^{3} = - 5 : x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

解为

x = 3 \frac{3}{2}, x = - 3 \frac{3}{2} \frac{1}{2} + 3 \frac{3}{2} \frac{3}{2} i, x = - 3 \frac{3}{2} \frac{1}{2} - 3 \frac{3}{2} \frac{3}{2} i, x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

作图

流行的例子

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