方程1/(x²+1)+(x²+1)/x²=10/3x的实数根

1/(x²+1)+(x²+1)/x²=10/(3x)
x/(x²+1)+(x²+1)/x=10/3
令x/(x²+1)=y,(x²+1)/x=1/y
那么y+1/y=10/3
y²-10/3y+1=0
解得y=3或y=1/3
由x/(x²+1)=3
==> 3x²-x+3=0
Δ=1-36x²-3x+1=0
==> x=(3-√5)/2或x=(3+√5)/2
所以方程为实数根为
x=(3-√5)/2或x=(3+√5)/2