Question Number 151383 by mathdanisur last updated on 20/Aug/21
$$\mathrm{if}\:\:\mathrm{x};\mathrm{y}>\mathrm{0}\:\:\mathrm{peove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}}{\mathrm{3}}\:\centerdot\:\frac{\mathrm{2}}{\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\centerdot\:\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\:\geqslant\:\mathrm{xy} \\ $$
Commented by mathdanisur last updated on 20/Aug/21
$$\mathrm{Thank}\:\mathrm{You}\:\mathrm{Dear}\:\boldsymbol{\mathrm{S}}\mathrm{er},\:\geqslant\sqrt[{\mathrm{3}}]{\mathrm{xy}}\:\mathrm{for}\:\mathrm{solution}\:\mathrm{please} \\ $$
Answered by dumitrel last updated on 20/Aug/21
Commented by mathdanisur last updated on 20/Aug/21
$$\mathrm{Nice}\:\mathrm{Dear}\:\boldsymbol{\mathrm{S}}\mathrm{er},\:\mathrm{Thank}\:\mathrm{You} \\ $$