Question

cho x,y không âm, cmr :

\(\dfrac{\sqrt{x-1}}{x}+\dfrac{\sqrt{y-1}}{y}\le1\)

Answer 1

\(\dfrac{1.\sqrt{x-1}}{x}+\dfrac{1.\sqrt{y-1}}{y}\le\dfrac{1+x-1}{2x}+\dfrac{1+y-1}{2y}=\dfrac{1}{2}+\dfrac{1}{2}=1\)

Dấu "=" xảy ra khi x=y=2