x 2 + y 2 2 ⩾ x + y 2 ⩾ x y ⩾ 2 1 x + 1 y {\displaystyle {\sqrt {\frac {x^{2}+y^{2}}{2}}}\geqslant {\frac {x+y}{2}}\geqslant {\sqrt {xy}}\geqslant {\frac {2}{{\frac {1}{x}}+{\frac {1}{y}}}}}