Question

[Dũng Nguyễn]

Cho \(\frac{a}{b}=\frac{c}{d}\)(b,d ko bằng 0). CM rằng \(\frac{ac}{bd}=\frac{a^2-c^2}{b^2-d^2}\)

Answer 1

[Nguyệt]

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

áp dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a^2-c^2}{b^2-d^2}\)

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a^2}{b^2}=\frac{a}{b}\cdot\frac{a}{b}=\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}\left(dpcm\right)\)

Answer 2

[Hoàng Ninh]

Có \(\frac{a}{b}=\frac{c}{d}\left(b,d\ne0\right)\)

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

\(\frac{a}{b}=\frac{c}{d}=\frac{a^2}{b^2}=\frac{a}{b}.\frac{c}{d}=\frac{a^2-c^2}{b^2-d^2}=\frac{ac}{bd}\)

Vậy \(\frac{ac}{bd}=\frac{a^2-c^2}{b^2-d^2}\)( đpcm )