>>823

Problem 2.
　Given real numbers x,y,z such that x+y+z=0, show that
　x(x+2)/(2x^2 +1) + y(y+1)/(2y^2 +1) + z(z+2)/(2z^2 +1) ≧ 0,
　When does equality hold ?

Problem 372.
For all a,b,c>0 and abc=1, prove that
　1/{a(a+1)+ab(ab+1)} + 1/{b(b+1)+bc(bc+1)} + 1/{c(c+1)+ca(ca+1)} ≧ 3/4.