Ext2 Inequalities: Algebraic Proof of HM-GM-AM-QM Inequality

We algebraically prove the chain of inequalities between the Harmonic Mean, Geometric Mean, Arithmetic Mean and Quadratic Means.

[@corytheman3165]

Thank you you explained it perfectly

[@jakubfrei3757]

Wow, very nice content mate. Thx

[@SimchaWaldman]

Nice writing!

[@techzbrothers2045]

a and b should be positive no. Inplace of non negative

[@MathemaEducation]

The inequality holds for zero as well.

[@davidmadsen2761]

​@@MathemaEducation Except for the harmonic mean

[@jameschan2404]

Hi can you tell me, from the first place how do you know what mapping to do?

[@MathemaEducation]

I guess a lot of it comes with experience. Knowing that the reciprocal of the harmonic mean can be written as 1/2(1/a+1/b) suggests that the arithmetic mean of 1/a and 1/b is in play. That's why I made a point to show this understanding of the harmonic mean at the end of the previous video. Hope that helps out a little bit :)

[@user-pg7uq7cv3d]

​@@MathemaEducation🎉🎉🎉🎉🎉🎉🎉