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AMC / AIME · AM-GM Inequality · Medium

AM-GM Inequality: If math and math, find the maximum of math.

Means inequality.

Try the problem

If a,b>0a,b>0 and a+b=6a+b=6, find the maximum of ab\sqrt{ab}.

Hint and answer

Concept to use

Equality cases.

Hint

For AM-GM, equality gives the extremum when terms are equal.

Answer

3

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