\(P=\dfrac{x^2+y^2}{x-y}=\dfrac{x^2-2xy+y^2+2xy}{x-y}\)
\(=\dfrac{\left(x-y\right)^2}{x-y}+\dfrac{2}{x-y}\)
\(=\left(x-y\right)+\dfrac{2}{x-y}\ge2\sqrt{\left(x-y\right)\cdot\dfrac{2}{x-y}}=2\sqrt{2}\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}\left(x-y\right)^2=2\\xy=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{\sqrt{6}+\sqrt{2}}{2}\\\dfrac{\sqrt{6}-\sqrt{2}}{2}\end{matrix}\right.\)
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