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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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a starting shot... | Comment 1 of 21
Well, I'm first noting that x is maximized when either y or z is 0. It doesn't matter which one is 0 due to the structure of the equations as they both lead to the same two variable equations with interchangable y and z. Solving these two two-variable equations yields an answer of x maximized at x = 5-√2 = 3.5857

This might make sense or I could just be talking out of my butt....
  Posted by DuCk on 2003-11-17 13:48:03
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