[latex] \left \{ {{1/ \sqrt{x} +1/ \sqrt{y}=1 } \atop { \sqrt{x} + \sqrt{y}=4}} \right. [/latex]

[latex] \left \{ {{ \frac{1}{ \sqrt{x} } + \frac{1}{ \sqrt{y} }=1 } \atop { \sqrt{x} + \sqrt{y}=4}} \right. \\\ \left \{ {{ \sqrt{x} =a} \atop { \sqrt{y} =b}} \right. \\\ \left \{ {{ \frac{1}{ a} + \frac{1}{ b }=1 } \atop {a +b=4}} \right. \\\ a=4-b \\\ \frac{1}{ 4-b} + \frac{1}{ b }=1 \\\ b+4-b=b(4-b) \\\ 4=4b-b^2 \\\ b^2-4b+4=0 \\\ (b-2)^2=0 \\\ b-2=0 \\\ b=2 \\\ a=4-2=2[/latex] [latex] \left \{ {{ \sqrt{x} =2} \atop { \sqrt{y} =2}} \right. \\\ \left \{ {{x=4} \atop { y=4} \right. [/latex] Ответ: (4; 4)