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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: another solution | Comment 11 of 21 |
(In reply to another solution by retiarius)

Solving the second equation for that X gives

√(19)(y+z) + yz = 3, but since y + z = 5-√(19), you can replace that.

25 - 5√(19) +yz = 3
22 - 5√(19) + yz = 0

This ends up with yz equalling negative; don't know if that's a problem though
  Posted by Gamer on 2003-11-18 18:13:10

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