Question

[Vô Danh]

1, Cho \(\dfrac{a+c}{b+d}\) = \(\dfrac{a-c}{b-d}\). C/M \(\dfrac{a^{2017}-c^{2017}}{b^{2017}-d^{2017}}\) = (\(\dfrac{a}{b}\))²⁰¹⁷

Answer 1

[Đoàn Thái Bảo]

Từ gt => (a+c)(b-d)=(b+d)(a-c)

nên ab+bc-ad-cd=ab+ad-bc-cd   =>   2bc=2ad     => bc=ad

=> \(\frac{a}{b}=\frac{c}{d}\) => \(\frac{a^{2017}}{b^{2017}}=\frac{c^{2017}}{d^{2017}}=\frac{a^{2017}-c^{2017}}{b^{2017}-d^{2017}}\)(theo t/c dãy tỉ số bằng nhau)