Question

cho tỉ lệ : \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\). chứng minh : \(\dfrac{a}{b}\)=\(\dfrac{7a+5c}{7b+5d}\) ( b + d khác 0 )

Answer 1

\(\dfrac{a}{b}=\dfrac{7a}{7b}\\ \dfrac{c}{d}=\dfrac{5c}{5d}\Rightarrow\dfrac{a}{b}=\dfrac{7a}{7b}=\dfrac{5c}{5d}\Rightarrow\dfrac{7a}{7b}=\dfrac{5c}{5d}\)

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

\(\dfrac{7a}{7b}=\dfrac{5c}{5d}=\dfrac{7a+5c}{7b+5d}\)

Mà \(\dfrac{7a}{7b}=\dfrac{a}{b}\Rightarrow\dfrac{a}{b}=\dfrac{5c}{5d}=\dfrac{7a+5c}{7b+5d}\Leftrightarrow\dfrac{a}{b}=\dfrac{7a+5c}{7b+5d}\)

Vậy \(\dfrac{a}{b}=\dfrac{7a+5c}{7b+5d}\left(đpcm\right)\)

Answer 2

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

\(\Rightarrow ad=bc\)

\(\Rightarrow5ad=5bc\)

\(\Rightarrow7ab+5ad=7ab+5bc\)

\(\Rightarrow a\left(7b+5d\right)=b\left(7a+5c\right)\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{7a+5c}{7b+5d}\rightarrowđpcm\)