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Home » Olympiad Section » Inequalities » Inequalities Unsolved Problems
 
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Difficult
Let x_i be a root of 4x^2-4xa_i+(a_i-1)^2\leq0
a_i \in [\frac{1}{2},5]
Prove that \sqrt{\frac{\sum\limits_{i=1}^n a_i^2}{n}}\leq\frac{\sum\limits_{i=1}^n a_i}{n}+1

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