Question

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

CMR.a, \(\dfrac{a-2b}{b}\)=\(\dfrac{c-2d}{d}\)

b,\(\dfrac{ac}{bd}\)=\(\dfrac{a^2-c^2}{b^2-d^2}\)

Answer 1

a,\(\dfrac{a-2b}{b}\)=\(\dfrac{c-2d}{d}\)

\(\Rightarrow\)\(\dfrac{a-b}{b}\)-1=\(\dfrac{c-d}{d}\)-1

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

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

Answer 2

b: Đặt a/b=c/d=k

=>a=bk; c=dk

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

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

Do đó: \(\dfrac{ac}{bd}=\dfrac{a^2-c^2}{b^2-d^2}\)