+0  
 
0
77
1
avatar

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

Guest May 13, 2018
 #1
avatar+945 
+2

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

 

We distribute the variables:

 

\(a^2+2ab=\frac{104}3,b^2+2bc=\frac79, \text{and} \ c^2+2ac=-7\)

 

Add the three equations:

 

\(a^2+b^2+c^2+2ab+2bc+2ac=\frac{104}{3}+\frac79-7\)

 

We recognize the left side of the equation as the expanded form of \((a+b+c)^2\)

 

We can rewrite the equation in the form like this:

 

\((a+b+c)^2=\frac{256}9 \)

 

Since the problem asks for \( |a+b+c|\), we take the square root:

 

\(\sqrt{(a+b+c)^2}=\sqrt{\frac{256}9}\\ a+b+c=\pm\frac{16}3 \)

 

Therefore, \( |a+b+c|=\boxed{\frac{16}3}\) 

 

I hope this helped,

 

Gavin

GYanggg  May 13, 2018

35 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.