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?
+505 Notice that \((x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\). You could multiply the second equation by 2 and then add the equations up:
\(x^2+y^2+z^2+2xy+2yz+2zx=9+6\cdot2\\(x+y+z)^2=21\)
Take the square root of both sides and you will arrive at the answer.
(notice that the negative square root is extraneous since x, y, and z are all nonnegative)
