Question

[Thảo Fami]

cho tỉ lẹ thức a/b = c/d . chứng tỏ  ab/cd = a^2 - b^2/c^2 - d^2

Answer 1

[T.Ps]

#)Giải :

Ta có :  \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{ab}{cd}=\frac{a^2+b^2}{c^2+d^2}=\frac{a^2-b^2}{c^2-d^2}\)

\(\Rightarrow\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}\left(đpcm\right)\)

Answer 2

[Cá Chép Nhỏ]

\(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\)(1)

Ta có : \(ab\left(c^2-d^2\right)=abc^2-abd^2=acbc-adbd\)(2)

            \(cd\left(a^2-b^2\right)=a^2cd-b^2cd=acad-bcbd\)(3)

Từ (1),(2),(3) => \(ab\left(c^2-d^2\right)=cd\left(a^2-b^2\right)\Rightarrow\text{đpcm}\)