Question

CẦN GẤP !!!

Answer 1

ĐKXĐ: \(x;y\ge0\)

\(P=\left(x+\dfrac{y}{4}+\dfrac{1}{4}-\sqrt{xy}-\sqrt{x}+\dfrac{\sqrt{y}}{2}\right)+\left(\dfrac{7}{4}y-\dfrac{\sqrt{y}}{2}+\dfrac{1}{28}\right)-\dfrac{2}{7}\)

\(P=\left(\sqrt{x}-\dfrac{\sqrt{y}}{2}-\dfrac{1}{2}\right)^2+\dfrac{7}{4}\left(\sqrt{y}-\dfrac{1}{7}\right)^2-\dfrac{2}{7}\ge-\dfrac{2}{7}\)

\(P_{min}=-\dfrac{2}{7}\) khi \(\left\{{}\begin{matrix}\sqrt{x}-\dfrac{\sqrt{y}}{2}-\dfrac{1}{2}=0\\\sqrt{y}-\dfrac{1}{7}=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{16}{49}\\y=\dfrac{1}{49}\end{matrix}\right.\)