Question

cho \(\frac{a}{b}=\frac{c}{d}\), chứng minh:

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

Answer 1

Ta có: \(\frac{a}{b}=\frac{c}{d}\)

=>\(\frac{a}{c}=\frac{b}{d}\)

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

=>\(\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{ab}{cd}\)

=>\(\frac{a^2-b^2}{c^2-d^2}=\frac{ab}{cd}=\frac{a^2}{c^2}\)(the t/c dãy TSBN) (đpcm)

Answer 2

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{a^2-b^2}{c^2-d^2}=\frac{a}{c}\times\frac{b}{d}=\frac{ab}{cd}\left[tc\right]\Rightarrow DieuPhaiChungMinh\)