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*}
# | User | Rating |
---|---|---|
1 | tourist | 3757 |
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 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 171 |
2 | awoo | 165 |
3 | adamant | 164 |
4 | TheScrasse | 159 |
5 | maroonrk | 155 |
6 | nor | 154 |
7 | -is-this-fft- | 152 |
8 | Petr | 147 |
9 | orz | 146 |
10 | pajenegod | 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*}
Name |
---|