\(Given that $a(a+2b) = \frac{104}3$, $b(b+2c) = \frac{7}{9}$, and $c(c+2a) = -7$, find $|a+b+c|$.\)
There are many solutions. One of them is:
a = 4, b = 7/3, c = -1, so:
a + b + c = 4 + 7/3 + (-1) = 16/3 =5 1/3
+5 
