Question

cho \(\frac{a}{b}\frac{c}{d}\left(b,c,d\ne0;c-2d\ne0\right).\)

chưng minh rằng:\(\frac{\left(a-2b\right)4}{\left(c-2d\right)^4}=\frac{a^{4+2017b^4}}{c^4+2017d^4}\)

Answer 1

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

\(\Rightarrow\frac{a^4}{c^4}=\frac{\left(a-2b\right)^4}{\left(c-2d\right)^4}\)mà\(\frac{a^4}{c^4}=\frac{b^4}{d^4}=\frac{2017b^4}{2017d^4}=\frac{a^4+2017b^4}{c^4+2017d^4}\)
=> đpcm