(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that:

0 <= A <= B

[tex] A \leq \sqrt{AB} \leq (A + B)/ 2 \leq B [/tex]

2. Relevant equations

root AB = geometric mean

(A + B)/ 2 = arithmetic mean

<= means less then or equal to.

3. The attempt at a solution

I managed to come up with something for the (A + B)/ 2 part.

a < = (a+a)/2 <= (a+b)/2 <= (b+b)/2 <= b

that shows that (a+b)/2 is less then b but greater then a. i can't figure out how to show that with root ab.

Any help would be great!

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# Homework Help: The AM-GM Inequality

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