Ta có: \(\dfrac{a}{c}=\dfrac{a}{b}.\dfrac{b}{c}\Rightarrow\dfrac{a}{c}=\left(\dfrac{a}{c}\right)^2=\left(\dfrac{b}{c}\right)^2=\dfrac{a^2}{b^2}=\dfrac{b^2}{c^2}=\dfrac{a^2+b^2}{b^2+c^2}\)
Vậy nếu có tỉ lệ thức \(\dfrac{a}{b}=\dfrac{b}{c}\) ta có tỉ lệ thức \(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)
\(\dfrac{a}{b}=\dfrac{b}{c}\Leftrightarrow b^2=ac\)
\(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a^2+ac}{ac+c^2}=\dfrac{a\left(a+c\right)}{c\left(c+a\right)}=\dfrac{a}{c}\)