solvable by SOS?

dyd · Hodge Conjecture Offline Joined: 02 Aug 2005 Posts: 63

For positive reals $x,y,z$ and reals $0<a\leq b\leq c$ ,
$b\left( \left( x+y+z\right) ^{2}-4zx\right) \left( c-a\right) ^{2}-4xyc\left( b-a\right) ^{2}-4yza\left( c-b\right) ^{2}\geq ...$

**Posted:** Sun Nov 01, 2009 10:54 am

_________________
I became a member just for messaging Very Happy

dyd · Hodge Conjecture Offline Joined: 02 Aug 2005 Posts: 63

No reply?

I'm learning how to use SOS but none of those 5 criteria is fulfilled. Am I missing something? Or maybe there's a counterexample?

**Posted:** Wed Nov 04, 2009 6:48 am

_________________
I became a member just for messaging Very Happy

can_hang2007

**Posted:** Wed Nov 04, 2009 5:06 pm

_________________
The love makes us stronger!

V. Q. B. Can

dyd · Hodge Conjecture Offline Joined: 02 Aug 2005 Posts: 63

Thanks!! Your proof makes me think twice before SOS-ing blindly without inspecting the condition of variables Blush

**Posted:** Thu Nov 05, 2009 2:26 am

_________________
I became a member just for messaging Very Happy