### Home > PC > Chapter 9 > Lesson 9.3.5 > Problem9-162

9-162.

Given that $a=x+\frac{1}{x}$, solve for $x$ in terms of $a$

Multiply each term by $x$.

$ax=x^2+1$

Move all terms to one side and set equal to $0$.

$x^2−ax+1=0$

$x=\frac{-(-a)\pm \sqrt{(-a)^2-4(1)(1)}}{2(1)}$