Answer
$y=-\frac{1}{5}$ or $y=\frac{1}{4}$
Work Step by Step
We simplify as follows:
$y^{-2}+y^{-1}=20$
Let $m=y^{-1}$
$m^{2}+m=20$
$m^{2}+m-20=0$
$(m+5)(m-4)=0$
$m+5=0$ or $m-4=0$
$m=-5$ or $m=4$
$y^{-1}=-5$ or $y^{-1}=4$
$\frac{1}{y}=-5$ or $\frac{1}{y}=4$
$y=-\frac{1}{5}$ or $y=\frac{1}{4}$
