Áp dụng bđt Cô si ta có:
\(\sqrt{x-2}\le\frac{x-2+1}{2}=\frac{x-1}{2}\)
\(\sqrt{y+2014}\le\frac{y+2014+1}{2}=\frac{y+2015}{2}\)
\(\sqrt{z-2015}\le\frac{z-2015+1}{2}=\frac{z-2014}{2}\)
Cộng theo vế: \(\sqrt{x-2}+\sqrt{y+2014}+\sqrt{z-2015}\le\frac{x-1+y+2015+z-2014}{2}=\frac{1}{2}\left(x+y+z\right)\)
Dấu "=" xảy ra khi: \(\hept{\begin{cases}x=3\\y=-2013\\z=2016\end{cases}}\)
Áp dụng bất đẳng thức Cô si ta có
\(\sqrt{x-2}\le\frac{x-2+1}{2}=\frac{x-1}{2}\)
\(\sqrt{y+2014}\le\frac{y+2014+1}{2}=\frac{y+2015}{2}\)
\(\sqrt{z-2015}\le\frac{z-2015+1}{2}=\frac{z-2014}{2}\)
Cộng theo vế
\(\sqrt{x-2}+\sqrt{y+2014}+\sqrt{z-2015}\le\)\(\frac{x-1+y+2015+z-2014}{2}=\frac{1}{2}\left(x+y+z\right)\)
Dấu = xảy ra khi
\(\hept{\begin{cases}x=3\\y=-2013\\z=2016\end{cases}}\)
