theo đầu bài ta có 2 TH:
TH1) a+b+c\(\ne\)0
ta có:
\(\dfrac{a+b-5c}{c}=\dfrac{b+c-5a}{a}=\dfrac{c+a-5b}{b}=\dfrac{a+b-5c+b+c-5a+c+a-5b}{c+a+b}\)
=\(\dfrac{-3a-3b-3c}{a+b+c}=\dfrac{-3\left(a+b+c\right)}{a+b+c}=-3\left(vìa+b+c\ne0\right)\)
Do đó:
\(\dfrac{a+b-5c}{c}=-3\)
=> a+b-5c=-3c
=> a+b=2c
Tương tự ta tính được : b+c=2a; a+c=2b (bạn làm chi tiết hơn)
M=\(\left(1+\dfrac{b}{a}\right)\left(1+\dfrac{c}{b}\right)\left(1+\dfrac{a}{c}\right)=\dfrac{a+b}{a}.\dfrac{b+c}{b}.\dfrac{a+c}{c}=\dfrac{2c}{a}.\dfrac{2a}{b}.\dfrac{2b}{a}=8\)
TH2) a+b+c=0
=>\(\left\{{}\begin{matrix}a+b=-c\\b+c=-a\\a+c=-b\end{matrix}\right.\)
=>\(M=-\dfrac{c}{a}.\dfrac{-a}{b}.\dfrac{-b}{c}=-1\)
Vậy M=-1 hoặc M=8