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

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**