Question

方程1/(x²+1)+(x²+1)/x²=10/3x的实数根

Answer 1

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