\(C=\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left[\left(\dfrac{1}{x}+\dfrac{1}{y}\right).\dfrac{1}{x+y+2\sqrt{xy}}+\dfrac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}\right)\right]\)(ĐKXĐ: \(x,y>0\))
\(C=\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left[\dfrac{x+y}{xy\left(\sqrt{x}+\sqrt{y}\right)^2}+\dfrac{2\sqrt{xy}}{xy\left(\sqrt{x}+\sqrt{y}\right)^2}\right]\)
\(C=\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\dfrac{1}{xy}=\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{xy}}\)
thay \(\left\{{}\begin{matrix}x=2-\sqrt{3}\\y=2+\sqrt{3}\end{matrix}\right.\) ta có:
\(C=\dfrac{\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}}{\sqrt{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}}=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
\(\sqrt{2}C=\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}=-2\)
\(\Rightarrow C=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
