Question

tìm n thuộc N :

2n + 3 chia hết cho 5n - 4 .

giúp mk nhanh m.n nhé !

Answer 1

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\(2n+3⋮5n-4\)

\(\Rightarrow5\left(2n+3\right)⋮5n-4\)

\(\Rightarrow10n+15⋮5n-4\)

\(\Rightarrow10n-8+23⋮5n-4\)

\(\Rightarrow2\left(5n-4\right)+23⋮5n-4\)

\(2\left(5n-4\right)⋮5n-4\Rightarrow23⋮5n-4\)

\(\Rightarrow5n-4\inƯ\left(23\right)=\left\{\pm1;\pm23\right\}\)

\(\Rightarrow\left[{}\begin{matrix}5n-4=1\\5n-4=-1\\5n-4=23\\5n-4=-23\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5n=5\\5n=3\\5n=27\\5n=-19\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}n=1\\n=\dfrac{3}{5}\\n=\dfrac{27}{5}\\n=-\dfrac{19}{5}\end{matrix}\right.\)

Vì \(n\in N\) nên \(n=1\)