Question Number 92151 by jagoll last updated on 05/May/20
$$\mathrm{If}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\mathrm{pq}\:+\:\mathrm{2p}+\mathrm{2q}\:=\:\mathrm{217}\: \\ $$$$\mathrm{find}\:\mathrm{p}+\mathrm{q}\: \\ $$
Commented by john santu last updated on 05/May/20
$$\Rightarrow\left({p}+\mathrm{2}\right)\left({q}+\mathrm{2}\right)\:=\:\mathrm{17}×\mathrm{13} \\ $$$${p}+\mathrm{2}+{q}+\mathrm{2}\:=\:\mathrm{30} \\ $$$${p}+{q}\:=\:\mathrm{26}\: \\ $$$$ \\ $$