Let \(a,b,c,d,e,f \) be nonnegative real numbers.

(a) Prove that \((a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) \ge (ace + bdf)^4.\)

(b) Prove that \((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2\)

littlemixfan May 16, 2020

#1

#3**0 **

I have not managed to prove it algebraically but here is a graphical demonstration where it certainly appears to be true.

https://www.desmos.com/calculator/djm2pyxgsh

this is part a)

Melody May 17, 2020