Question

 CMR : ƯCLN (2n + 5; 2n + 4 ) = 1

 

Answer 1

Gọi: d = ƯCLN ( 2n + 5; 2n + 4 ) ; \(d\in N\)*

\(\Rightarrow\hept{\begin{cases}2n+5⋮d\\2n+4⋮d\end{cases}\Rightarrow}\left(2n+5\right)-\left(2n+4\right)⋮d\)

\(\Rightarrow1⋮d\)

\(\Rightarrow d=1\)

Vậy:  ƯCLN ( 2n + 5; 2n + 4 ) = 1 ( đpcm )

Answer 2

Có 2n+5 luôn luôn lẻ

     2n+4 luôn luôn chẵn

Suy ra 2n+5,2n+4 nguyên tố cùng nhau

hay UCLN ( 2n+5,2n+4 )=1(đpcm)