Question

Cho \(\frac{a+b}{c}\)=\(\frac{a+c}{b}\)=\(\frac{b+c}{a}\) và a, b, c≠0

Tính M=(1+\(\frac{a}{b}\))(1+\(\frac{b}{c}\))(1+\(\frac{c}{a}\))

Answer 1

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

\(\Rightarrow\left\{{}\begin{matrix}a+b=2c\\a+c=2b\\b+c=2a\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}a+b+c=0\\a=b=c\end{matrix}\right.\)

- Nếu \(a+b+c=0\)

\(\Rightarrow M=\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\frac{\left(-c\right)\left(-a\right)\left(-b\right)}{abc}=-1\)

- Nếu \(a=b=c\Rightarrow M=\left(1+1\right)\left(1+1\right)\left(1+1\right)=8\)