Question

[nguyen thanh lan]

tìm GTNN của

C= x -2 căn xy+ 3y-2 căn x +1

giúp dùm mình đi ạk

Answer 1

[pham trung thanh]

\(C=x-2\sqrt{xy}+3y-2\sqrt{x}+1\)à

Answer 2

[pham trung thanh]

\(C=x-2\sqrt{xy}+3y-2\sqrt{x}+1\)

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

\(=\left(\sqrt{x}-\sqrt{y}\right)^2-2\left(\sqrt{x}-\sqrt{y}\right)+1+2\left(y-\sqrt{y}+\frac{1}{4}\right)-\frac{1}{2}\)

\(=\left(\sqrt{x}-\sqrt{y}-1\right)^2+2\left(\sqrt{y}-\frac{1}{2}\right)^2-\frac{1}{2}\ge\frac{-1}{2}\)

Đến đây dễ rồi