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受欢迎的代数 >

-50-w(w^3-9w)=0

解答

- 50 - w (w^{3} - 9 w) = 0

解答

w = \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i

求解步骤

- 50 - w (w^{3} - 9 w) = 0

展开

- 50 - w (w^{3} - 9 w) : - 50 - w^{4} + 9 w^{2}

- 50 - w^{4} + 9 w^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- w^{4} + 9 w^{2} - 50 = 0

用

u = w^{2}

和

u^{2} = w^{4}

改写方程式

- u^{2} + 9 u - 50 = 0

解

- u^{2} + 9 u - 50 = 0 : u = \frac{9}{2} - i \frac{119}{2}, u = \frac{9}{2} + i \frac{119}{2}

u = \frac{9}{2} - i \frac{119}{2}, u = \frac{9}{2} + i \frac{119}{2}

代回

u = w^{2}

，求解

w

解

w^{2} = \frac{9}{2} - i \frac{119}{2} : w = \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i

解

w^{2} = \frac{9}{2} + i \frac{119}{2} : w = \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i

解为

w = \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i

作图

流行的例子

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