Question

cho a/b=c/d, chung minh:

a²-b²/c²-d²=ab/cd

                              Thanks nhiu!!!!!!!! ( vs dieu kien phai giup mk cai da)

Answer 1

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a^2}{b^2}=\frac{c^2}{d^2}\)\(\Rightarrow\frac{a^2}{b^2}-1=\frac{c^2}{d^2}-1\)

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

\(\Rightarrow\frac{a^2-b^2}{c^2-d^2}=\frac{b^2}{d^2}\left(1\right)\)

Ta lại có :\(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{ab}{b^2}=\frac{cd}{d^2}\Rightarrow\frac{ab}{cd}=\frac{b^2}{d^2}\left(2\right)\)

Từ (1) và (2)\(\Rightarrow\frac{a^2-b^2}{c^2-d^2}=\frac{ab}{cd}\)