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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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Solution re: solution - corrected, I think | Comment 8 of 21 |
(In reply to solution by Charlie)

It's a good thought, and Charlie made an algebraic mistake (I think).

It *can* be simplified to -y² + (5-x)y + 5x - x² - 3 = 0 (He forgot the -3).

Continue with this... find the descriminant, and I think you'll find the bounds to be 5/3 ± 8/3. And the higher of the two is 13/3, which agrees with what I wrote earlier.

--- SK
Edited on November 17, 2003, 5:18 pm
  Posted by SilverKnight on 2003-11-17 17:17:00

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