Question

方程1/(x^2+1)+(x^2+1)/x^2=10/（3x）的实数根

Answer 1

x不等于0

方程两边都乘以x

x/(x^2+1)+(x^2+1)/x=10/3

设x/(x^2+1)=y

方程变为

y+1/y=10/3

3y^2-10y+3=0

y1=3,y2=1/3

1)x/(x^2+1)=3时,无实数解

2)x/(x^2+1)=1/3时,

x1=(3+根号5)/2,x2=(3-根号5)/2,