Let x, y, z be integers such that x^2 + y^2 + z^2 = 18 and xy + yz + zx = 9. Find |x| + |y| + |z|.
x^2 + y^2 + z^2 = 18 xy + yz + zx = 9
x^2 + y^2 = 18 - z^2
Here are the possibilities for x, y and z (in any order)
x y z
1 4 1
-1 - 4 -1
3 3 0
-3 -3 0
So
l x l + l y l + l z l = 6
