Answer
${(-2,-4), (-2, 4), (2, -4), (2,4)}$
Work Step by Step
$x^2+y^2=20$
$xy=8$
$xy=8$
$xy/x=8/x$
$y=8/x$
$x^2+y^2=20$
$x^2+(8/x)^2=20$
$x^2+64/x^2=20$
$w=x^2$
$x^2+64/x^2=20$
$w+64/w=20$
$w*(w+64/w)=w*20$
$w^2+64=20w$
$w^2+64-20w=20w-20$
$w^2-20w+64=0$
$(w-16)(w-4)=0$
$w=x^2$
$(w-16)(w-4)=0$
$(x^2-16)(x^2-4)=0$
$x^2-16=0$
$x^2-16+16=0+16$
$x^2=16$
$\sqrt {x^2} =\sqrt {16}$
$x= ±4$
$x^2-4=0$
$x^2-4+4=0+4$
$x^2=4$
$\sqrt {x^2} =\sqrt 4$
$x=±2$
$x=±4$
$x^2+y^2=20$
$16+y^2=20$
$16+y^2-16=20-16$
$y^2=4$
$\sqrt {y^2} = \sqrt 4$
$y =±2$
$y=±4$
$x^2+y^2=20$
$16+x^2=20$
$16+x^2-16=20-16$
$x^2=4$
$\sqrt {x^2} = \sqrt 4$
$x =±2$
