Giải thích các bước giải:
$A=(x+\dfrac{1}{x})^2+(y+\dfrac{1}{y})^2$
$\rightarrow A\ge \dfrac{1}{2}(x+\dfrac{1}{x}+y+\dfrac{1}{y})^2$
$\rightarrow A\ge \dfrac{1}{2}(x+\dfrac{1}{x}+y+\dfrac{1}{y})^2$
$\rightarrow A\ge \dfrac{1}{2}(x+y+\dfrac{1}{x}+\dfrac{1}{y})^2$
$\rightarrow A\ge \dfrac{1}{2}(x+y+\dfrac{4}{x+y})^2$
$\rightarrow A\ge \dfrac{1}{2}(4(x+y)+\dfrac{4}{x+y}-3)^2$
$\rightarrow A\ge \dfrac{1}{2}(2\sqrt{4(x+y).\dfrac{4}{x+y}}-3)^2$
$\rightarrow A\ge \dfrac{1}{2}.5^2$
$\rightarrow A\ge \dfrac{25}{2}$
$\rightarrow MinA=\dfrac{25}{2}\rightarrow x=y=\dfrac{1}{2}$
