[nooonuii]

ข้อ 5 ครับ

\[ a^2b^2(a+b) \leq \frac{a^4+b^4}{2} (a+b) \leq a^5 + b^5 \]

\[ a^2b^2(a+b+c) = a^2b^2(a+b) + a^2b^2c =a^2b^2(a+b) + ab \leq a^5+b^5 +ab \]

\[ \frac{ab}{a^5+b^5+ab} \leq \frac{1}{ab(a+b+c)} \]

\[ \frac{ab}{a^5+b^5+ab} + \frac{bc}{b^5+c^5+bc} + \frac{ca}{c^5+a^5+ca} \leq \frac{1}{a+b+c} (\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}) = \frac{1}{abc} = 1 \]