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Ta có: $\dfrac{1}{x}$+$\dfrac{1}{y}$=$\dfrac{1}{2}$

\Leftrightarrow2(x+y)=xy

Áp dụng BĐT Cauchy cho 2 số dương ta có: x+y\geq$2\sqrt{xy}$

\Rightarrowxy\geq$4\sqrt{xy}$\Leftrightarrow$\sqrt{xy}$\geq4

A=$x^{\frac{1}{2}}+y^{\frac{1}{2}}$=$\sqrt{x}$ + $\sqrt{y}$

Áp dụng BĐT Cauchy: $\sqrt{x}+\sqrt{y}$\geq2$\sqrt{\sqrt{xy}}$ \geq $2\sqrt{4}$=4

Vậy $A_{min}$=4\Leftrightarrowx=y=4
 
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