<s>[INST] Find the value of $(a+b-c)/(a+b+c)$ 
Given $$2a^2 +17b^2 + 8c^2 -6ab -20bc =0 \\ abc \neq 0.$$ 
  Find the value of $(a+b-c)/(a+b+c)$.

I tried factorizing the equation, but still can't find a solution
 [/INST] $$0=2\cdot LHS=(2a-3b)^2+(5b-4c)^2$$
and so $2a=3b$ and $5b=4c$. This gives $$\frac{a+b-c}{a+b+c}=\frac{3b/2+b+5b/4}{3b/2+b-5b/4}=1/3.$$
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