Câu hỏi 196
Cho $a$, $b$, $c$ là số thực dương. Giả sử rằng $$
\frac{a^{19}}{b^{19}} + \frac{b^{19}}{c^{19}} + \frac{c^{19}}{a^{19}} \leq \frac{a^{19}}{c^{19}} + \frac{b^{19}}{a^{19}} + \frac{c^{19}}{b^{19}}
$$ chứng minh rằng $$
\frac{a^{20}}{b^{20}} + \frac{b^{20}}{c^{20}} + \frac{c^{20}}{a^{20}} \leq \frac{a^{20}}{c^{20}} + \frac{b^{20}}{a^{20}} + \frac{c^{20}}{b^{20}}
$$
\frac{a^{19}}{b^{19}} + \frac{b^{19}}{c^{19}} + \frac{c^{19}}{a^{19}} \leq \frac{a^{19}}{c^{19}} + \frac{b^{19}}{a^{19}} + \frac{c^{19}}{b^{19}}
$$ chứng minh rằng $$
\frac{a^{20}}{b^{20}} + \frac{b^{20}}{c^{20}} + \frac{c^{20}}{a^{20}} \leq \frac{a^{20}}{c^{20}} + \frac{b^{20}}{a^{20}} + \frac{c^{20}}{b^{20}}
$$