Question

2 cách nhé, một cách cx đc

cho a/b=c/d chung minh (a+b)^2019/(c+d)2019=a^2019+b^2019/c^2019+d^2019

 

 

Answer 1

#)Giải :

Ta có : \(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\Rightarrow\frac{a^{2019}}{c^{2019}}=\frac{b^{2019}}{d^{2019}}=\frac{a^{2019}+b^{2019}}{c^{2019}+d^{2019}}\left(1\right)\)

Lại có : \(\frac{a^{2019}}{c^{2019}}=\frac{b^{2019}}{d^{2019}}=\left(\frac{a}{c}\right)^{2019}=\left(\frac{b}{d}\right)^{2019}=\left(\frac{a+b}{c+d}\right)^{2019}=\frac{\left(a+b\right)^{2019}}{\left(c+d\right)^{2019}}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\frac{\left(a+b\right)^{2019}}{\left(c+d\right)^{2019}}=\frac{a^{2019}+b^{2019}}{c^{2019}+d^{2019}}\left(đpcm\right)\)