Question

Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}\) . Chứng minh rằng a=b=c

Answer 1

Ta có: \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}\)

*\(\dfrac{a}{b}=\dfrac{b}{c}\)\(\Leftrightarrow\)a.c=b.b\(\Rightarrow\)a=c

*\(\dfrac{b}{c}=\dfrac{c}{a}\)\(\Leftrightarrow\)b.a=c.c\(\Rightarrow\)b=a

Kết luận: a=b=c

Answer 2

vì a/b=b/c=c/a

=> (a+b+c)/(b+c+a)=1

=>a=b=c(đpcm)

Answer 3

\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}=\dfrac{a+b+c}{b+c+a}=1\\ \Rightarrow\left\{{}\begin{matrix}a=b\\b=c\\c=a\end{matrix}\right.\Rightarrow a=b=c\left(đpcm\right)\)