Difference between revisions of "2016 JBMO Problems/Problem 2"

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(Problem)
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== 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>.

Revision as of 00:55, 23 April 2018

Problem

Let $a,b,c$ be positive real numbers.Prove that

$\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3}$.

Solution

See also

2016 JBMO (ProblemsResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4
All JBMO Problems and Solutions
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