Prove that for any $$$a, b, c>0$$$ the following inequality is true: \begin{align*} \left(\frac{a^2+b^2+c^2}{3}\right)\left(\frac{b^3}{a}+\frac{c^3}{b}+\frac{a^3}{c}\right) \ \ge a(2b-a)+b(2c-b)+c(2a-c) \end{align*}
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 3690 |
2 | jiangly | 3647 |
3 | Benq | 3581 |
4 | orzdevinwang | 3570 |
5 | Geothermal | 3569 |
5 | cnnfls_csy | 3569 |
7 | Radewoosh | 3509 |
8 | ecnerwala | 3486 |
9 | jqdai0815 | 3474 |
10 | gyh20 | 3447 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | maomao90 | 174 |
2 | awoo | 164 |
3 | adamant | 163 |
4 | TheScrasse | 159 |
5 | nor | 157 |
6 | maroonrk | 155 |
7 | -is-this-fft- | 152 |
8 | Petr | 146 |
8 | orz | 146 |
10 | BledDest | 145 |
A math problem
Prove that for any $$$a, b, c>0$$$ the following inequality is true: \begin{align*} \left(\frac{a^2+b^2+c^2}{3}\right)\left(\frac{b^3}{a}+\frac{c^3}{b}+\frac{a^3}{c}\right) \ \ge a(2b-a)+b(2c-b)+c(2a-c) \end{align*}
Название |
---|