(adsbygoogle = window.adsbygoogle || []).push({}); 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 !

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# Homework Help: Triangle Inequality Proof

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