Let's Prove The AM-GM Inequality

[@md.eftekharahmed3865]

Your proof is easy to understand ❤

[@paultoutounji3582]

What a cool proof ! Bravo !

[@ShortsOfSyber]

Thanks!

[@DihinAmarasigha-up5hf]

Ah...finally a great understandable proof for the Am Gm Inequality

[@ShortsOfSyber]

😊

[@yoav613]

Nice proof

[@ShortsOfSyber]

Thank you!

[@grrgrrgrr0202]

You can prove a much more general statement by first proving the inequality for weighted means of two elements. I.e. t*a + (1-t)*b >= a^t*b^(1-t), with a,b>0 and t in (0,1). Fix t and b and let f(a) be the difference (which we wanna prove to be nonnegative). We first look at f' and find that f'(a) = t - t*a^(t-1)*b^(1-t). We see that f'(a)=0 at a=b. Furthermore, f' increases so f'(a)

[@ΕκπαιδευτήριαΚαντά-η1ω]

cube ID x^3+ψ^3+z^3-3xψz=1/2(x+ψ+z){(x-ψ)^2+(ψ-z)^2+(z-x)^2}>=0 x^3+ψ^3+z^3>=3xψz if a=qubx b=qubψ z=qubz we proved identity cauchy for three qub means three root

[@insaromarov1462]

Bro u could do it easier (x+y+z)³>=27xyz and then by am gm

[@ShortsOfSyber]

Why? 😁

[@yakupbuyankara5903]

X=Y=Z=3