Question

Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}\left(a,b,c\ne0\right).aCMRa=b=c\)

Answer 1

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

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

\(\Rightarrow a=b=c\)

Answer 2

Ta có:

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

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

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

\(\dfrac{b}{c}=1\Rightarrow b=c\) ( 2 )

\(\dfrac{c}{a}=1\Rightarrow c=a\) ( 3 )

Từ ( 1 ) ; ( 2 ) ; ( 3 ) => a = b = c.

Answer 3

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

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

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

=> A=B=C