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受欢迎的代数 >

63-27w^2+2w^4=0

解答

63 - 27 w^{2} + 2 w^{4} = 0

解答

w = \frac{21}{2}, w = - \frac{21}{2}, w = 3, w = - 3

+1

十进制

w = 3.24037 \dots, w = - 3.24037 \dots, w = 1.73205 \dots, w = - 1.73205 \dots

求解步骤

63 - 27 w^{2} + 2 w^{4} = 0

改写成标准形式

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

2 w^{4} - 27 w^{2} + 63 = 0

用

u = w^{2}

和

u^{2} = w^{4}

改写方程式

2 u^{2} - 27 u + 63 = 0

解

2 u^{2} - 27 u + 63 = 0 : u = \frac{21}{2}, u = 3

u = \frac{21}{2}, u = 3

代回

u = w^{2}

，求解

w

解

w^{2} = \frac{21}{2} : w = \frac{21}{2}, w = - \frac{21}{2}

解

w^{2} = 3 : w = 3, w = - 3

解为

w = \frac{21}{2}, w = - \frac{21}{2}, w = 3, w = - 3

作图

流行的例子

x^{3} - x^{2} - 3 x - 1 = 0

8 w^{3} + 2 w - 1 = 0

m^{3} + m^{2} - m - 1 = 0

x^{2} - 6 = 6 - x^{3}

x^{4} - 2 x^{2} + a = 0