Question

Cho \(\dfrac{b+c}{a}=\dfrac{c+a}{b}=\dfrac{a+b}{c}\)

CMR : \(a-b=0\) hoặc \(a+b+c=0\)

Answer 1

\(\dfrac{b+c}{a}=\dfrac{c+a}{b}=\dfrac{a+b}{c}\)

\(\Rightarrow\dfrac{b+c}{a}+1=\dfrac{c+a}{b}+1=\dfrac{a+b}{c}+1\)

\(\Rightarrow\dfrac{a+b+c}{a}=\dfrac{a+b+c}{b}=\dfrac{a+b+c}{c}\)

Từ \(\dfrac{a+b+c}{a}=\dfrac{a+b+c}{b}\Leftrightarrow a\left(a+b+c\right)=b\left(a+b+c\right)\)

\(\Rightarrow\left(a-b\right)\left(a+b+c\right)=0\)

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