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受欢迎的代数 >

10x^4-11x^2+3=0

解答

10 x^{4} - 11 x^{2} + 3 = 0

解答

x = \frac{3}{5}, x = - \frac{3}{5}, x = \frac{1}{2}, x = - \frac{1}{2}

+1

十进制

x = 0.77459 \dots, x = - 0.77459 \dots, x = 0.70710 \dots, x = - 0.70710 \dots

求解步骤

10 x^{4} - 11 x^{2} + 3 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

10 u^{2} - 11 u + 3 = 0

解

10 u^{2} - 11 u + 3 = 0 : u = \frac{3}{5}, u = \frac{1}{2}

u = \frac{3}{5}, u = \frac{1}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{3}{5} : x = \frac{3}{5}, x = - \frac{3}{5}

解

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

解为

x = \frac{3}{5}, x = - \frac{3}{5}, x = \frac{1}{2}, x = - \frac{1}{2}

作图

流行的例子

x^{3} - 4 x + 6 = 0

765=400*(1+x)^6

765 = 400 \cdot (1 + x)^{6}

x^3-x^2-10x+10=0

x^{3} - x^{2} - 10 x + 10 = 0

8 x^{3} = 3 x^{2}

- 4 = - 64 r^{5 - 1}