srikanth

• Dec 1st, 2005

 

A

NITraj

• Jul 24th, 2006

 

take x=y=z=1/3then xy+yz+zx=1/3 < 1/2

vishal

• Jul 18th, 2007

 

<1/2

because

 (x + y + z)^2 - (x^2 + y^2 + z^2) = 2(xy + yz + zx)

that shows that the

  (x + y + z)^2 - (x^2 + y^2 + z^2) * (1/2) = xy + yz + zx

so first term is devided by two and also less then (x^2 + y^2 + z^2) so it has some fractional value less then one. so obvious the answer is the less then the half.