Question

$left { {{1/ sqrt{x} +1/ sqrt{y}=1 } atop { sqrt{x} + sqrt{y}=4}} right.$

Answer 1

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