Originally Posted by

**nathan02079** $\displaystyle \frac{x^2+1}{x}+\frac{x}{x^2+1}=2.9$

Substitution: $\displaystyle z=\frac{x^2+1}{x}$

$\displaystyle z+\frac{1}{z}=2.9$

$\displaystyle z^2-2.9z+1=0$

$\displaystyle z_1,_2=\frac{2.9\mp\sqrt{4.41}}{2}$

$\displaystyle z_1=2.5$

$\displaystyle z_2=0.4$

So

$\displaystyle 2.5=\frac{x^2+1}{x}$

$\displaystyle x_1,_2=\frac{2.5\mp\sqrt{2.25}}{2}$

$\displaystyle x_1=2$

$\displaystyle x_2=0.5$

and

$\displaystyle 0.4=\frac{x^2+1}{x}$

$\displaystyle x^2-0.4x+1=0$

$\displaystyle x_3,_4=\frac{0.4\mp\sqrt{0.16-4}}{2}$

Which brings us to no solution

Is this right?