Question

$frac{1}{ sqrt{x} } + frac{1}{ sqrt{y} } = 4 - sqrt{x} - sqrt{y}$

Answer 1

1/корень(х)+1/корень(у)=4-(корень(х)+корень(у))
1/корень(х)-2+корень(х)=2-(1/корень(у)+корень(у))
1/корень(х)-2+корень(х)=-(1/корень(у)-2+корень(у))
(х^(-1/4)-х^(1/4))^2=-(y^(-1/4)-y^(1/4))^2
(х^(-1/4)-х^(1/4))^2 >= 0
(y^(-1/4)-y^(1/4))^2 >= 0
=>х^(-1/4)-х^(1/4) = 0 и y^(-1/4)-y^(1/4)=0
********************
х^(-1/4)-х^(1/4) = 0
х^(-1/2)-2+х^(1/2) = 0
х^(-1)+2+х^(1) = 4
х^(-1)+х^(1) = 2
1/х + х = 2
х^2-2x+1 = 0
x=1
********аналогично***********
y^(-1/4)-y^(1/4) = 0
..........
у=1
*********************
ответ х=у=1