Hello all, I've been struggling with the following problem:

We have \( p,q,r,s,t \)and \(u\) as nonnegative real numbers.

i. Show that \((p^2 + q^2)^2 (r^4 + s^4)(t^4 + u^4) ≥ (prt + qsu)^4.\)

ii. Show that \((p^2 + q^2)(r^2 + s^2)(t^2 + u^2) ≥ (prt + qsu)^2.\)

So far I have put \(r^2, s^2, t^2\) and \(u^2\) into the Cauchy-Schwarz form : \((r^4+s^4)(t^4+u^4)\geq(r^2t^2+s^2u^2)^2\); but after this I don't know how to continue. I also have no idea where to begin for part ii. Please help, I'm very confused!

Guest Jul 25, 2020