Two more problems

1. Find the least value of the expression $(x+y)(y+z)$, given that $x,y,z$ are positive numbers satisfying the equation $xyz(x+y+z) = 1$. (U.S.S.R. Olympiad 1989 #21)
2. Find the minimum value of $$(u-v)^2 +\left(\sqrt{2-u^2} - \frac{9}{v}\right)^2$$ for $0<u<\sqrt{2}$ and $v>0$. (1984 Putnam Exam B2 and BAMM 1999 #16)

If you have comments, questions or find glaring errors, please contact me by e-mail at the following address: trike@ousd.k12.ca.us