Indians primary school math

maximum if x=y

so, 2y^6=54 => y=sqrt(3) and x=sqrt(3)

x*y=3

By the AM-GM inequality: $54=x^6+y^6\geq 2\sqrt{x^6y^6}=2(xy)^3$ $\Rightarrow 2(xy)^3\leq 54$ $\Rightarrow xy \leq 3$ The maximum value $3$ (of $xy$ ) can be achieved when $x=y=\sqrt{3}$ .