Show that $2 xy < x^2 + y^2$ for $x$ is not equal to $y$ Show that $2 xy < x^2 + y^2$ for $x$ is not equal to $y$.

If $x\neq y$ then without loss of generality we can assume that $x>y$  $x-y>0\Rightarrow (x-y)^2>0\Rightarrow x^2-2xy+y^2>0\Rightarrow x^2+y^2>2xy$
