[Toán 9] giúp mình với

H

hiensau99

Gọi ƯCLN(21n +4; 14n+3)=d [TEX]\\d \in N*[/TEX]
Ta có: [TEX]21n +4 \vdots d; 14n+3 \vdots d[/TEX] \Rightarrow [TEX]2.(21n +4) \vdots d;\ 3.(14n+3) \vdots d[/TEX]
\Rightarrow [TEX]2.(21n +4) - 3.(14n+3) \vdots d[/TEX]
\Rightarrow [TEX] 42n+8-42n-9 \vdots d [/TEX]
\Rightarrow [TEX] -1 \vdots d[/TEX]
\Rightarrow d=1
Vậy ƯCLN(21n +4; 14n+3)=1

 
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