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Ta có \(x\inℕ\Rightarrow x\ge0\Rightarrow x+1\ge1>0\Rightarrow\frac{1}{x+1}\le\frac{1}{1}=1\)
Dấu = xảy ra \(\Leftrightarrow x=0\left(tm\right)\)
Vậy GTLN 1/x+1 =1 tại x=0
Để \(\frac{3n+4}{n-1}\)là số nguyên thì:
\(3n+4⋮n-1\)
Mà \(3\left(n-1\right)⋮n-1\)
nên \(3n+4-3\left(n-1\right)⋮n-1\\ \Rightarrow7⋮n-1\)
\(\Rightarrow\left(n-1\right)\inƯ\left(7\right)=\left\{1;-1;7;-7\right\}\)
\(\Rightarrow n\in\left\{2;0;8;-6\right\}\)
Bài kia bạn nhân 3n+1 lên 2 lần rồi làm tương tự
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\(\frac{x+6}{x+1}=\frac{x+1+5}{x+1}=1+\frac{5}{x+1}\in N\)
\(\Leftrightarrow x+1\inƯ\left(5\right)\Leftrightarrow x+1\in\left\{1;5\right\}\)
\(\Leftrightarrow x\in\left\{0;4\right\}\)