d) 26 = 2 . 13
38 = 2 . 19
ƯCLN(26,38) = 2
ƯC(26,38) = Ư(2) = 1,2
Mà theo đề bài : 26 ⋮ (x-1) ; 38 ⋮ (x-1)
Nên : x = 2 hoặc 3
\(26⋮\left(x-1\right);38⋮\left(x-1\right)\Rightarrow x-1\inƯC\left(26,38\right)=\left\{\pm2;\pm1\right\}\Rightarrow x\in\left\{-1;0;2;3\right\}\)
Mà x là số tự nhiên \(\Rightarrow x\in\left\{0;2;3\right\}\)
\(\Rightarrow\left(x-1\right)\inƯC\left(26,38\right)=Ư\left(2\right)=\left\{1;2\right\}\\ \Rightarrow x\in\left\{2;3\right\}\)