Question

CMR:Nếu \(\dfrac{a}{b}\)=\(\dfrac{b}{c}\)=\(\dfrac{c}{a}\)thì a=b=c

Answer 1

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

Áp dụng tính chất dãy tỉ số bằng nhau, ta có:

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

\(\Rightarrow\dfrac{a}{b}=1\Leftrightarrow a=b\)

\(\Rightarrow\dfrac{b}{c}=1\Leftrightarrow b=c\)

\(\Rightarrow\dfrac{c}{a}=1\Leftrightarrow a=c\)

vậy a=b=c => đpcm

Answer 2

https://hoc24.vn/hoi-dap/question/646533.html