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受欢迎的代数 >

x^{10}-10x^2+5=0

解答

x^{10} - 10 x^{2} + 5 = 0

解答

x = \frac{3.14517 E 14}{6.25 E 14}, x = - \frac{3.14517 E 14}{6.25 E 14}, x = \frac{4.05431 E 15}{2.5 E 15}, x = - \frac{4.05431 E 15}{2.5 E 15}

+1

十进制

x = 0.70938 \dots, x = - 0.70938 \dots, x = 1.27346 \dots, x = - 1.27346 \dots

求解步骤

x^{10} - 10 x^{2} + 5 = 0

用

u = x^{2}

和

u^{5} = x^{10}

改写方程式

u^{5} - 10 u + 5 = 0

解

u^{5} - 10 u + 5 = 0 : u \approx 0.50322 \dots, u \approx 1.62172 \dots, u \approx - 1.88596 \dots

u \approx 0.50322 \dots, u \approx 1.62172 \dots, u \approx - 1.88596 \dots

代回

u = x^{2}

，求解

x

解

x^{2} = 0.50322 \dots : x = \frac{3.14517 E 14}{6.25 E 14}, x = - \frac{3.14517 E 14}{6.25 E 14}

解

x^{2} = 1.62172 \dots : x = \frac{4.05431 E 15}{2.5 E 15}, x = - \frac{4.05431 E 15}{2.5 E 15}

解

x^{2} = - 1.88596 \dots : x \in R

无解

解为

x = \frac{3.14517 E 14}{6.25 E 14}, x = - \frac{3.14517 E 14}{6.25 E 14}, x = \frac{4.05431 E 15}{2.5 E 15}, x = - \frac{4.05431 E 15}{2.5 E 15}

作图

流行的例子

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