Question

Chứng minh rằng: Nếu a/b=c/d thì \(\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\left(\frac{a-b}{c-d}\right)^{2014}\)

Answer 1

 

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\) Theo t/c dãy tỷ số băng nhau ta có

\(\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\left(\frac{a-b}{c-d}\right)^{2014}=\frac{a^{2014}}{c^{2014}}=\frac{b^{2014}}{d^{2014}}\) Theo t/c dãy tỷ số bằng nhau

\(\left(\frac{a-b}{c-d}\right)^{2014}=\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}\) (dpcm)

Answer 2

v~ cay wa đề mình là (a+b)^2014/(c+d)^2014= a^2014+b^2014/ c^2014+d^2014