Answer
$x = 2±2\sqrt{3}$
Work Step by Step
$\frac{1}{x^2}-\frac{4}{x}+1=0$
Multiply both sides by the least common multiple $x^2$
$\frac{1}{x^2}⋅x^2-\frac{4}{x}⋅x^2+1⋅x^2=0⋅x^2$
$1-4x+x^2=0$
Use the quadratic formula: $x = \frac{-b±\sqrt{b^2-4ac}}{2a}$
$a=1$, $b=-4$, $c=1$
$x = \frac{-(-4)±\sqrt{(-4)^2-(4⋅1⋅1)}}{(2⋅1)}$
$x = \frac{4±\sqrt{12}}{2}$
$x = \frac{4±4\sqrt{3}}{2}$
$x = 2±2\sqrt{3}$
