Ta có: \(P=\frac{x}{\sqrt{xy}+y}+\frac{y}{\sqrt{xy}-x}-\frac{x+y}{\sqrt{xy}}\)
\(=\frac{x}{\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)}+\frac{y}{\sqrt{x}\left(\sqrt{y}-\sqrt{x}\right)}-\frac{x+y}{\sqrt{xy}}\)
\(=\frac{x\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)-y\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)-\left(x+y\right)\left(x-y\right)}{\sqrt{xy}\left(x-y\right)}\)
\(=\frac{x^2-x\sqrt{xy}-y\sqrt{xy}-y^2-x^2+y^2}{\sqrt{xy}\left(x-y\right)}=\frac{\sqrt{xy}\left(-x-y\right)}{\sqrt{xy}\left(x-y\right)}=\frac{-x-y}{x-y}\)
\(=-\frac{\left(x+y\right)}{x-y}\)
Ta có: x+y=7
xy=10
Do đó: x,y là các nghiệm của phương trình:
\(A^2-7A+10=0\)
=>(A-2)(A-5)=0
=>A=2 hoặc A=5
TH1: x=2; y=5
\(A=-\frac{\left(x+y\right)}{x-y}\)
\(=-\frac{2+5}{2-5}=-\frac{7}{-3}=\frac73\)
TH2: x=5; y=2
\(A=-\frac{\left(x+y\right)}{x-y}\)
\(=-\frac{5+2}{5-2}=-\frac73\)
