1. The problem statement, all variables and given/known data Given:0 <= a <= b a <= Sqrt(ab) <= (a+b)/2 <= b 2. Relevant equations 3. The attempt at a solution The only problem im having prooving this inequality is Sqrt(ab) <= (a+b)/2. I have an idea but im not sure if it validates. can i do this.. ? (a+b)/2 - sqrt(ab) >= 0 if it is greater than 0 [ i get an answer of 1/4 (a-b)^2 >= 0 ] , (a+b)/2 must be greater than sqrt(ab). given that both sqrt(ab) and (a+b)/2 are >= 0 since 0 < a < b. Is my reasoning correct? or wrong please help !