Difference between revisions of "2016 JBMO Problems/Problem 2"
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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>. | ||
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{{JBMO box|year=2016|num-b=1|num-a=3|five=}} | {{JBMO box|year=2016|num-b=1|num-a=3|five=}} | ||
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| + | [[Category:Intermediate Algebra Problems]] | ||
be positive real numbers. Prove that
.
