If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have ?

(In reply to a starting shot... by DuCk)

xy+yz+zx=3 is a hyperboloid of two sheets that intersects the plane x+y+z=5 in a circle, but its center lies along an axis of x=y=z and is therefore diagonal to all the axes. Thus you can't take one of the variables as zero.

A good way to visualize this is to use David Parker's DPGraph software, which is a lot cheaper than Mathematica, but produces 3-D graphs of things like this, including both surfaces.

See www.davidparker.com.

Posted by Charlie on 2003-11-17 14:15:32