Question

Giúp mình với

Answer 1

Đặt A= x+y+\(\dfrac{1}{2x}+\dfrac{2}{y}\)

Ta có: A= \(x+y+\dfrac{1}{2x}+\dfrac{2}{y}\) = \(\left(\dfrac{x}{2}+\dfrac{1}{2x}\right)+\left(\dfrac{y}{2}+\dfrac{2}{y}\right)+\dfrac{x}{2}+\dfrac{y}{2}\)

\(\geq\) \(2\sqrt{\dfrac{x}{2}.\dfrac{1}{2x}}+2\sqrt{\dfrac{y}{2}.\dfrac{2}{y}}+\dfrac{x+y}{2}\) \(\geq\) \(1+2+\dfrac{3}{2}=\dfrac{9}{2}\)

Dấu = xảy ra khi x=1;y=2