ข้อ 1. $L.S. = \frac{2}{(a^2+b^2)+2a+2}+\frac{2}{(b^2+c^2)+2b+2}+\frac{2}{(c^2+a^2)+2c+2} $
By A.M.-G.M.
$ L.S. \leqslant \frac{2}{2ab+2a+2}+\frac{2}{2bc+2b+2}+\frac{2}{2ac+2c+2} $
$ \leqslant \frac{1}{ab+a+1}+\frac{1}{bc+b+1}+\frac{1}{ac+c+1} $
เพราะว่า $ abc=1 $ ได้ว่า $ c=\frac{1}{ab} $
$ L.S. \leqslant \frac{1}{ab+a+1}+\frac{1}{\frac{1}{a}+b+1 }+\frac{1}{\frac{1}{b}+\frac{1}{ab}+1 } = \frac{1+a+ab}{ab+a+1} = 1 $
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