An algebra problem by U Z

$x^{8} + y^{8}$ +6 = 8xy

now lets apply am-gm in $x^{8} + y^{8}$ +6

$\frac{x^{8} + y^{8} +1 +1 +1 +1+1+1}{8}$ $\geq$ xy

thus we get $x^{8} + y^{8}$ +6 $\geq$ 8xy

case of minimum value therefore x ={+1, -1}

y = {+1,-1}

hence 2 pairs