Question

[Thao_army_2002]

Giải phương trình

\(\sqrt{x-2}\)+\(\sqrt{y+2009}\)+\(\sqrt{z-2010}\)=\(\frac{1}{2}\left(x+y+z\right)\)

Answer 1

[alibaba nguyễn]

Ta có \(1\sqrt{x-2}\le\frac{1+x-2}{2}=\frac{x-1}{2}\)

\(1\sqrt{y+2009}\le\frac{1+y+2009}{2}=\frac{y+2010}{2}\)

\(1\sqrt{z-2010}\le\frac{1+z-2010}{2}=\frac{z-2009}{2}\)

Cộng vế theo vế ta được

\(1\sqrt{x-2}+\sqrt{y+2009}+\sqrt{z-2010}\)

\(\le\)\(\frac{x+y+z}{2}\)

Đấu = xảy ra khi x = 3; y = - 2008; z = 2011