Question Number 197636 by universe last updated on 25/Sep/23
Answered by mr W last updated on 25/Sep/23
$${s}={x}+{y} \\ $$$$\left({x}+\mathrm{3}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\left(\mathrm{8}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\left({x}+\mathrm{3}\right)^{\mathrm{2}} +\left({s}−{x}\right)^{\mathrm{2}} =\mathrm{128} \\ $$$$\mathrm{2}\left({x}+\mathrm{3}\right)+\mathrm{2}\left({s}−{x}\right)\left(−\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{s}=\mathrm{2}{x}+\mathrm{3} \\ $$$$\left({x}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{2}{x}+\mathrm{3}−{x}\right)^{\mathrm{2}} =\mathrm{128} \\ $$$$\Rightarrow{x}+\mathrm{3}=\mathrm{8}\: \\ $$$$\Rightarrow{x}=\mathrm{5}\: \\ $$$$\Rightarrow{s}_{{max}} =\mathrm{2}×\mathrm{5}+\mathrm{3}=\mathrm{13}\:\checkmark \\ $$
Commented by universe last updated on 25/Sep/23
$${thanks}\:{sir} \\ $$