IF a,b >0

prove: AM - GM >= GM - HM

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- Jun 6th 2006, 02:57 PMSusie38More with AM and GM
IF a,b >0

prove: AM - GM >= GM - HM - Aug 26th 2006, 08:49 PMRebesques
If I get it right, u need to show that for all a,b>0,

.

Both sides are positive; Begin calculating until you get to a valid inequality.

(remember AM>GM>HM.) - Nov 21st 2006, 05:35 PMputnam120

from here we just have to apply AM-GM. Note that .

if you don't know AM-GM, basically it just states: for any we are assured that , with equality iff (if and only if) .

Challenge: Prove that for all nonnegative x and y that

try not to use the fact that