Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\),Chứng minh \(\dfrac{a^2}{b^2}=\dfrac{a.c}{b.d}\)

Answer 1

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=>\(a=bk\),\(c=dk\)

\(\dfrac{a^2}{b^2}=\dfrac{bk^2}{b^2}=k^2\left(1\right)\)

\(\dfrac{ac}{bd}=\dfrac{bk.dk}{bd}=k^2\left(2\right)\)

Từ (1) và (2)=>\(\dfrac{a^2}{b^2}=\dfrac{ac}{bd}\)(đpcm)

Answer 2

Đặt \(\dfrac{a}{b}=k;\dfrac{c}{d}=k\)

\(\Rightarrow a=kb;c=kd\)

\(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{bk^2}{b^2}=k^2\)

\(\Rightarrow\dfrac{ac}{bd}=\dfrac{bkdk}{bd}=k^2\)

Từ các chứng minh trên cho ta thấy

\(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{a.c}{b.d}\)

Answer 3

Đặt:

\(\dfrac{a}{b}=\dfrac{c}{d}=k\) \(\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

\(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{bk^2}{b^2}=k^2\)

\(\dfrac{ac}{bd}=\dfrac{bk.dk}{bd}=\dfrac{k^2bd}{bd}=k^2\)

\(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{ac}{bd}\Rightarrowđpcm\)