Answer
$y=-1/5, 1/4$
Work Step by Step
$y^{-2} + y^{-1} = 20$
$y^{-1} = x$
$y^{-2} + y^{-1} = 20$
$y^{-1*2} + y^{-1} = 20$
$x^2 +x=20$
$x^2+x-20=20-20$
$x^2+x-20=0$
$(x+5)(x-4)=0$
$x+5=0$
$x+5-5=0-5$
$x=-5$
$x-4=0$
$x-4+4=0+4$
$x=4$
$y^{-1} = x$
$1/y =x$
$1/y*y/x=x*y/x$
$1/x =y$
$x=-5$
$1/x =y$
$1/-5=y$
$-1/5 =y$
$x=4$
$1/x =y$
$1/4=y$
