Hello, I've come across a problem in my textbook that really baffles me.

Task: to use substitution $\displaystyle u=x+1/x$ to solve the equation for x:

$\displaystyle x^2+3x-2+3/x+1/x^2=0$

It was easy to make the quadratic equation,

$\displaystyle u^2+3u-2=0$

$\displaystyle u1= (-3+sqrt(17))/2$

$\displaystyle u2=(-3-sqrt(17))/2$

but solving for x was a bit "ugly" (quoted because math is NOT ugly

)

$\displaystyle x+1/x=(-3+sqrt(17))/2$

$\displaystyle x+1/x=(-3-sqrt(17))/2$

I've spent quite a time over this, any pointers?