Difference between revisions of "2014 USAJMO Problems"
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===Problem 1=== | ===Problem 1=== | ||
| + | Let <math>a</math>, <math>b</math>, <math>c</math> be real numbers greater than or equal to <math>1</math>. Prove that <cmath>\min{\left (\frac{10a^2-5a+1}{b^2-5b+1},\frac{10b^2-5b+1}{c^2-5c+10},\frac{10c^2-5c+1}{a^2-5a+10}\right )}\leq abc </cmath> | ||
[[2014 USAJMO Problems/Problem 1|Solution]] | [[2014 USAJMO Problems/Problem 1|Solution]] | ||
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===Problem 2=== | ===Problem 2=== | ||
[[2014 USAJMO Problems/Problem 2|Solution]] | [[2014 USAJMO Problems/Problem 2|Solution]] | ||
Revision as of 17:09, 29 April 2014
Contents
Day 1
Problem 1
Let 
, 
, 
be real numbers greater than or equal to 
. Prove that ![\[\min{\left (\frac{10a^2-5a+1}{b^2-5b+1},\frac{10b^2-5b+1}{c^2-5c+10},\frac{10c^2-5c+1}{a^2-5a+10}\right )}\leq abc\]](http://latex.artofproblemsolving.com/3/a/d/3ad6f9ab816469889e5b8452f203c0e9b01647f4.png)
Solution
