Question Number 160644 by HongKing last updated on 03/Dec/21
$$\mathrm{King}'\mathrm{s}\:\mathrm{inequality} \\ $$$$\mathrm{if}\:\:\:\mathrm{a}\leqslant\mathrm{b}\:\:\:;\:\:\:\mathrm{n}\leqslant\mathrm{m}\:\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{a}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{m}}} }{\mathrm{2}}\:\geqslant\:\left(\frac{\mathrm{1}\:+\:\mathrm{b}}{\mathrm{2}}\right)^{\boldsymbol{\mathrm{m}}-\boldsymbol{\mathrm{n}}} \:\centerdot\:\left(\frac{\mathrm{a}\:+\:\mathrm{b}}{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} \\ $$