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 \((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2\)
It's easy! Just appy Markus's inequality.
I have not managed to prove it algebraically but here is a graphical demonstration where it certainly appears to be true.
this is part a)