Question Number 116538 by Khalmohmmad last updated on 04/Oct/20
$$\mathrm{x}+\sqrt{\mathrm{y}}=\mathrm{11} \\ $$$$\sqrt{\mathrm{x}}−\mathrm{y}=\mathrm{24} \\ $$$$\mathrm{x},\mathrm{y}=? \\ $$
Commented by mr W last updated on 04/Oct/20
$${no}\:{real}\:{solution}! \\ $$$${x}\geqslant\mathrm{0},\:{y}\geqslant\mathrm{0} \\ $$$${x}+\sqrt{{y}}=\mathrm{11}\:\Rightarrow{x}\leqslant\mathrm{11} \\ $$$$ \\ $$$$\mathrm{24}+{y}=\sqrt{{x}}\leqslant\sqrt{\mathrm{11}}=\mathrm{3}.\mathrm{3}\:\:\:…\left({i}\right) \\ $$$$\mathrm{24}+{y}\geqslant\mathrm{24}\:\:\:…\left({ii}\right) \\ $$$$\left({i}\right)\:{and}\:\left({ii}\right)\:{are}\:{contradiction}! \\ $$
Commented by MJS_new last updated on 04/Oct/20
$$\mathrm{no}\:\mathrm{solution}\:\mathrm{in}\:\mathbb{C} \\ $$