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\[ \large{\begin{cases} x^2+y^2+z^2=18 \\ xy+yz+zx = 9 \end{cases}} \]

Let \(x,y\) and \(z\) be integers satisfying the system of equations above. Find \( |x| + |y| + |z| \).

 Jan 30, 2021
 #1
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(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. :)))

 

=^._.^=

 Jan 30, 2021

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