IF a,b >0 prove: AM - GM >= GM - HM

Follow Math Help Forum on Facebook and Google+

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.)

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