Question

[Phạm Lợi]

Cho x>0,y>0 , x+y\(\ge\)6 .tim gia tri nho nhat cua bieu thuc p=3x+2y+6/x+8/y

Answer 1

[Nguyễn Việt Lâm]

\(P=3x+2y+\dfrac{6}{x}+\dfrac{8}{y}=\dfrac{3x}{2}+\dfrac{6}{x}+\dfrac{y}{2}+\dfrac{8}{y}+\dfrac{3}{2}\left(x+y\right)\)

\(\Rightarrow P\ge2\sqrt{\dfrac{3x}{2}.\dfrac{6}{x}}+2\sqrt{\dfrac{y}{2}.\dfrac{8}{y}}+\dfrac{3}{2}.6=19\)

\(\Rightarrow P_{min}=19\) khi \(\left\{{}\begin{matrix}x=2\\y=4\end{matrix}\right.\)