Question Number 124314 by liberty last updated on 02/Dec/20
$$\begin{cases}{{x}\sqrt{{x}}\:+{y}\sqrt{{y}}\:=\:\mathrm{19}}\\{{x}\sqrt{{y}}\:+{y}\sqrt{{x}}\:=\:\mathrm{15}}\end{cases}.\:{find}\:{x}+{y} \\ $$$$\:\begin{cases}{{x}\sqrt{{x}}\:+{y}\sqrt{{y}}\:=\:\mathrm{133}}\\{{y}\sqrt{{x}}\:−\:{x}\sqrt{{y}}\:=\:\mathrm{30}}\end{cases}.\:{find}\:{x}+{y}+{xy} \\ $$$$\:\begin{cases}{\sqrt{{x}}\:+{y}\:=\:\mathrm{53}}\\{{x}\:+\:\sqrt{{y}}\:=\:\mathrm{23}}\end{cases}.\:{find}\:{x}+{y} \\ $$
Commented by Dwaipayan Shikari last updated on 02/Dec/20
$$\sqrt{{x}}+{y}=\mathrm{53} \\ $$$${x}+\sqrt{{y}}\:=\mathrm{23}\:\:\:\:\:\:\:{x}=\mathrm{16}\:,{y}=\mathrm{49}\:\:\left({By}\:{observation}\right) \\ $$