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 \((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2.\)
I believe Cauchy-Schwarz could be helpful, but am confused. Please help!
