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Three numbers (Posted on 2003-11-17) Difficulty: 3 of 5
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 ?

No Solution Yet Submitted by Ravi Raja    
Rating: 3.7500 (4 votes)

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re(2): solution - corrected, I think | Comment 9 of 21 |
(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

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