Rút gọn \(\dfrac{\sqrt{x+\sqrt{x^2-y^2}+}\sqrt{x-\sqrt{x^2-y^2}}}{\sqrt{2\left(x-y\right)}}\) (x > y > 0 )

F = \(\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left[\left(\dfrac{1}{x}+\dfrac{1}{y}\right).\dfrac{1}{x+y+2\sqrt{xy}}+\dfrac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}\right)\right]\)

Phan tích : \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

Chứng minh \(\sqrt{101}-\sqrt{99}>0,1\)