Cauchy Schwarz Help

[mathman29]

Hello,
I have something like this:

(q²+r²)²(s⁴+t⁴)(u⁴+v⁴) >= (qsu + rtv)⁴

I used Cauchy Schwarz to get:

((qs)²+(rt)²)(u²+v²) >= (qsu+rtv)²

I was thinking about squaring both sides so I get (qsu + rtv)⁴ but then the algebra seems to become a mess. Any input? thanks.

 

[Steven G]

What topic did this problem come from? That would be really helpful to know.

I would do the multiplication for both sides. Neither is bad, unless you do not know the binomial theorem for the rhs.