Question

Cho (a + c)(b - d) = (a - c)(b + d)

Chứng minh rằng:a/b=c/d

Answer 1

\(\left(a+c\right)\left(b-d\right)=\left(a-c\right)\left(b+d\right)\)

\(\Leftrightarrow ab-ad+bc-cd=ab+ad-bc-cd\)

\(\Leftrightarrow-ad+bc=ad-bc\)

\(\Leftrightarrow2bc=2ad\)

\(\Leftrightarrow bc=ad\)

\(\Leftrightarrow\frac{a}{b}=\frac{c}{d}\) (đpcm)

Answer 2

\(\left(a+b\right)\left(b-d\right)=\left(a-c\right)\left(b+d\right)\)

\(\Leftrightarrow\frac{a+c}{b+d}=\frac{a-c}{b-d}\) (Tính chất dãy tỉ số bằng nhau)

\(\Rightarrow\frac{a}{b}=\frac{c}{d}\) (đpcm)