\(C=x-2\sqrt{xy}+3y-2\sqrt{x}+1\)à
\(C=x-2\sqrt{xy}+3y-2\sqrt{x}+1\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2+2y-2\left(\sqrt{x}-\sqrt{y}\right)-2\sqrt{y}+1\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2-2\left(\sqrt{x}-\sqrt{y}\right)+1+2\left(y-\sqrt{y}+\frac{1}{4}\right)-\frac{1}{2}\)
\(=\left(\sqrt{x}-\sqrt{y}-1\right)^2+2\left(\sqrt{y}-\frac{1}{2}\right)^2-\frac{1}{2}\ge\frac{-1}{2}\)
Đến đây dễ rồi
tui giải rồi khó là \(\sqrt{a}-\sqrt{y}-1=0\) =0 khi nào?? á
\(\sqrt{y}-\frac{1}{2}=0\Rightarrow\sqrt{y}=\frac{1}{2}\Rightarrow y=\frac{1}{4}\)
\(\sqrt{x}-\sqrt{y}-1=0\)
\(\Rightarrow\sqrt{x}-\frac{1}{2}-1=0\Rightarrow\sqrt{x}=\frac{3}{2}\Rightarrow x=\frac{9}{4}\)
\(a-2\sqrt{ay}+3y-2\sqrt{a}+1\) 1 \(=\left(\sqrt{y^2}+1-\sqrt{a}^2+2\sqrt{y}-2\sqrt{a}\right)+\left(2y-2\sqrt{y}+\frac{1}{4}\right)-\frac{1}{4}\) =\(\left(\sqrt{y}+1-\sqrt{a}\right)^2+\left(\sqrt{2y}-\frac{1}{2}\right)^2-\frac{1}{4}\ge-\frac{1}{4}\) GTNN là -1/4 khi \(\hept{\begin{cases}\sqrt{2y}-\frac{1}{2}=0\Leftrightarrow y=\frac{1}{16}\\\sqrt{y}+1-\sqrt{a}=0\Leftrightarrow??\end{cases}}\)