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受欢迎的代数 >

x^4-5x^2+5=0

解答

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

解答

x = \frac{5 + 5}{2}, x = - \frac{5 + 5}{2}, x = \frac{5 - 5}{2}, x = - \frac{5 - 5}{2}

+1

十进制

x = 1.90211 \dots, x = - 1.90211 \dots, x = 1.17557 \dots, x = - 1.17557 \dots

求解步骤

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

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - 5 u + 5 = 0

解

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

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

代回

u = x^{2}

，求解

x

解

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

解

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

解为

x = \frac{5 + 5}{2}, x = - \frac{5 + 5}{2}, x = \frac{5 - 5}{2}, x = - \frac{5 - 5}{2}

作图

流行的例子

2 = (1 + r)^{7}

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20000=17100*(1+x)^3

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