Ta có: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{b+c+a}=1\)
\(\Rightarrow\hept{\begin{cases}\frac{a}{b}=1\\\frac{b}{c}=1\\\frac{c}{a}=1\end{cases}\Rightarrow\hept{\begin{cases}a=b\\b=c\\c=a\end{cases}\Rightarrow}a=b=c}\)
Mà a=2012 => b=c=2012
Có \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}\left(a+b+c\ne0;a=2012\right)\)
\(\Rightarrow\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=\frac{a+b+c}{b+c+a}=1\)
\(\Rightarrow\hept{\begin{cases}\frac{a}{b}=1\\\frac{b}{c}=1\\\frac{c}{a}=1\end{cases}}\Rightarrow a=b=c=2012\)
Vậy b;c = 2012
a/b = b/c = c/a
=> (a/b)^3 = abc/abc = 1
=> a = b = c = 2012
