Ta có :
\(\dfrac{a-b}{a+b}=\dfrac{a+b-2b}{a+b}=\dfrac{a+b}{a+b}-\dfrac{2b}{a+b}=1-\dfrac{2b}{a+b}\)
\(\dfrac{b-c}{b+c}=\dfrac{b+c-2c}{b+c}=\dfrac{b+c}{b+c}-\dfrac{2c}{b+c}=1-\dfrac{2c}{b+c}\)
Mà \(\dfrac{a-b}{a+b}=\dfrac{b-c}{b+c}\)
\(\Leftrightarrow1-\dfrac{2b}{a+b}=1-\dfrac{2c}{b+c}\)
\(\Leftrightarrow\dfrac{b}{a+b}=\dfrac{c}{b+c}\)
\(\Leftrightarrow b^2+bc=ac+bc\)
\(\Leftrightarrow b^2=ac\left(đpcm\right)\)
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