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integers

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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
+425
+1

(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