\[ \large{\begin{cases} x^2+y^2+z^2=18 \\ xy+yz+zx = 9 \end{cases}} \]
Let \(x,y\) and \(z\) be integers satisfying the system of equations above. Find \( |x| + |y| + |z| \).
(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx
Now, we just need to plug in some values.
(x+y+z)^2 = 18 + 2*9
(x+y+z)^2 = 36
x+y+z = 6
*Note that x+y+z could be -6, but we're looking for absolute value.
So our answer is 6. :)))
=^._.^=
