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 a starting shot...
My thoughts are to multiply the first equation by 3, the second equation by 5, and set them equal to each other (they're both equal to 15).
Then solve for X, and find the gradient.
Solve for the gradient =0...
I did some "back of the napkin" calculations... and I find that max x = 13/3, while y = z = 1/3.
I, admittedly did the problem quick and dirty... I hope someone will do this on his own and verify this work.