Question Number 9527 by Joel575 last updated on 12/Dec/16
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$${x}^{\mathrm{2}{n}} \:\geqslant\:\left({x}−\mathrm{1}\right)^{\mathrm{2}{n}} \:+\:\left(\mathrm{2}{x}−\mathrm{1}\right)^{{n}} \\ $$$${x}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{2}},\:\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integers} \\ $$