Question Number 152791 by mathdanisur last updated on 01/Sep/21
Answered by MJS_new last updated on 02/Sep/21
$$\left({xy}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{16}\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)\geqslant\mathrm{0} \\ $$$${x}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{18}{xy}+\mathrm{16}{x}+\mathrm{16}{y}−\mathrm{15}\geqslant\mathrm{0} \\ $$$${x}=\mathrm{3}+{p}\wedge{y}=\mathrm{3}+{q}\wedge{p}\geqslant\mathrm{0}\wedge{q}\geqslant\mathrm{0} \\ $$$${p}^{\mathrm{2}} {q}^{\mathrm{2}} +\mathrm{6}{pq}\left({p}+{q}+\mathrm{3}\right)+\mathrm{9}\left({p}^{\mathrm{2}} +{q}^{\mathrm{2}} \right)+\mathrm{16}\left({p}+{q}\right)\geqslant\mathrm{0} \\ $$$$\mathrm{which}\:\mathrm{obviously}\:\mathrm{is}\:\mathrm{true} \\ $$