Question

Answer 1

\(\left(\sqrt{x}-1\right)^2+\left(\sqrt{y}-1\right)^2\ge0\)

\(\Leftrightarrow x+y\ge2\left(\sqrt{x}+\sqrt{y}\right)-2=2\)

Đồng thời:

\(2=\sqrt{x}+\sqrt{y}\ge2\sqrt{\sqrt{xy}}\Rightarrow xy\le1\)

\(\Rightarrow\sqrt{xy}\le1\)

\(\Rightarrow-\sqrt{xy}\ge-1\)

Từ đó:

\(P\ge2-2022.1=-2020\)

\(P_{min}=2020\) khi \(x=y=1\)