Question: Let a, b, c, d, e, f be nonnegative real numbers.
Part A: Prove that \((a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) \ge (ace + bdf)^4.\)
Part B: Prove that \((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2.\)
The squares and same number of terms on each side makes me think we're supposed to use Cauchy to solve. However, I tried expanding parts A and B and the only thing i got were these large, nonsencial, unhelpful strings of terms.
Could someone please help me make these equations more Cauchy-friendly?