Hi all,
Please help to prove that: (sqr(xy)+sqr(yz)+sqr(xz))^2 >= 3sqr(3)xyz with: x, y, z are positive numbers and x + y + z = xyz.
Thanks.
Hi all,
Please help to prove that: (sqr(xy)+sqr(yz)+sqr(xz))^2 >= 3sqr(3)xyz with: x, y, z are positive numbers and x + y + z = xyz.
Thanks.
Apologies if im missing something, but can you confirm this is the proposition:
subject to:
x,y,z >0
xyz = x + y + z.
There are plenty of counter examples, eg:
x=500
y = 1
z = 501/499
(xyz = x+ y + z = 502.004008 as required.)
LHS = 2094.722
RHS = 2608.489