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 re: solution - corrected, I think by SilverKnight)

I confirm that x=13/3 is the solution. In addition to being the high end boundary for any of the variables such that the others don't go complex, it is also the ``calculus" answer that you obtain by solving for x as a function of y, setting the derivative wrt y equal to 0, and solving for y. You get y=1/3 or 3, of which the 1/3 gives x=13/3, z=1/3 or x=1/3, z=13/3 and the 3 gives x=3, z=-1 or x=-1, z=3.

Posted by Richard on 2003-11-18 00:40:16