Question

Cho các số thực dương a, b, c thỏa mãn a+ b+ c=6. CMR: \(\frac{b+c+5}{1+a}+\frac{c+a+4}{2+b}+\frac{a+b+3}{3+c}\ge6\)

Answer 1

\(P=\frac{b+c+5}{1+a}+\frac{c+a+4}{2+b}+\frac{a+b+3}{3+c}\)

\(\Rightarrow P+3=\frac{b+c+5}{1+a}+1+\frac{c+a+4}{2+b}+1+\frac{a+b+3}{3+c}+1\)

\(\Rightarrow P+3=\frac{a+b+c+6}{1+a}+\frac{a+b+c+6}{2+b}+\frac{a+b+c+6}{3+c}\)

\(\Rightarrow P+3=\frac{12}{1+a}+\frac{12}{2+b}+\frac{12}{3+c}\ge\frac{12.9}{6+a+b+c}=9\)

\(\Rightarrow P\ge6\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}a=3\\b=2\\c=1\end{matrix}\right.\)

Answer 2

này là dấu gì @Nguyễn Việt Lâm

Answer 3