[latex] frac{1}{ sqrt{x} } + frac{1}{ sqrt{y} } = 4 - sqrt{x} - sqrt{y} [/latex]

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) = 0х^(-1/2)-2+х^(1/2) = 0х^(-1)+2+х^(1) = 4х^(-1)+х^(1) = 21/х + х = 2х^2-2x+1 = 0x=1********аналогично***********y^(-1/4)-y^(1/4) = 0..........у=1*********************ответ х=у=1