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Given that \(a(a+2b) = \frac{104}3\)\(b(b+2c) = \frac{7}{9},\) and \(c(c+2a) = -7,\) find \(|a+b+c|.\)

 Sep 7, 2020
 #2
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Rewrite the equations as:

 

a^2 + 2ab = 104/3

b^2 + 2bc = 7/9

c^2 + 2ac = -7

 

Add them up:

 

a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = 256/9

 

But a^2 + b^2 + c^2 + 2ab + 2bc + 2ac =  (a + b + c)^2

 

so  (a + b + c)^2 = 256/9

 

hence |a + b + c| = 16/3

 Sep 7, 2020

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