Question

Answer 1

Áp dụng t/c dtsbn:

\(\dfrac{a+b-c}{c}=\dfrac{a-b+c}{b}=\dfrac{-a+b+c}{a}=\dfrac{a+b-c+a-b+c-a+b+c}{a+b+c}=\dfrac{2\left(a+b+c\right)}{a+b+c}=2\)

\(\Rightarrow\left\{{}\begin{matrix}a+b-c=2c\\a-b+c=2b\\-a+b+c=2a\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a+b=3c\\a+c=3b\\b+c=3a\end{matrix}\right.\)

\(M=\dfrac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\dfrac{3c.3b.3a}{abc}=\dfrac{27abc}{abc}=27\)