ATRACTOR

\(a,b,c,d>0\)

1. \(a+\frac{1}{a}\geq?\)
2. \(\frac{a+b}{2}(\geq or\leq?)\sqrt{ab}\)
3. \(\frac{a+b}{2}(\geq or\leq?)\sqrt{ab}\) (another version)
4. \(2ab(\geq or\leq?)a^{2}+b^{2}\)
5. \(ab+bc+ca(\geq or\leq?)a^{2}+b^{2}+c^{2}\)
6. \(\frac{a}{b}<\frac{c}{d}\Rightarrow\frac{a}{b}<?<\frac{c}{d}\)
7. Cauchy-Schwarz inequality \(|px+qy|\leq?\)