The non-negative real numbers x ,y and z satisfy the two equations
x^2 + y^2 + z^2 = 9
xy + yz + zx = 6
What is the sum of x, y, and z?
x^2 + y^2 + z^2 + 2(xy + yz + zx) = (x + y + z) ^2
= 21 = (x + y + z)^2
x + y + z = sqrt(21)
(Make sure you know why it's positive sqrt(21)!)
