Question Number 215137 by hardmath last updated on 29/Dec/24
$$\mathrm{If}\:\:\:\overline {\mathrm{ab}}\:+\:\overline {\mathrm{ba}}\:=\:\mathrm{n}^{\mathrm{2}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{max}\left(\mathrm{a}\centerdot\mathrm{b}\right)\:−\:\mathrm{min}\left(\mathrm{a}\centerdot\mathrm{b}\right)\:=\:? \\ $$
Answered by mahdipoor last updated on 29/Dec/24
$${ab}+{ba}=\mathrm{11}\left({a}+{b}\right)=\mathrm{11}^{\mathrm{2}} ={n}^{\mathrm{2}} \:\Rightarrow\mathrm{11}={a}+{b}\:\Rightarrow\: \\ $$$${max}\left({a}.{b}\right)=\mathrm{30}\:,\:{min}\left({a}.{b}\right)=\mathrm{18}\:\Rightarrow\:\mathrm{30}−\mathrm{18}=\mathrm{12} \\ $$