Difference between revisions of "2016 JBMO Problems/Problem 2"
(→See also) |
Ellentilburg (talk | contribs) (→Problem) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | Let <math>a,b,c </math>be positive real numbers.Prove that | + | Let <math>a,b,c</math> be positive real numbers. Prove that |
<math>\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3}</math>. | <math>\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3}</math>. | ||
be positive real numbers. Prove that
.
