Question

so cac gia tri n biet

A = \(\frac{8.n+193}{4.n+3}\)

tap hop cac gia tri n theo thu tu tang dan S\(\in\)..........

Answer 1

Giải:

Để A\(\in\)Z thì \(8.n+193⋮4.n+3\)

Ta có:
\(8.n+193⋮4.n+3\)

\(\Rightarrow\left(8.n+6\right)+187⋮4.n+3\)

\(\Rightarrow4.\left(n+3\right)+187⋮4n+3\)

\(\Rightarrow187⋮4n+3\)

\(\Rightarrow4n+3\in\left\{\pm1;\pm187\right\}\)

+) \(4n+3=1\Rightarrow n=\frac{-1}{2}\)

+) \(4n+3=-1\Rightarrow n=-1\)

+) \(4n+3=187\Rightarrow n=46\)

+) \(4n+3=-187\Rightarrow n=\frac{-85}{2}\)

Vậy các giá trị n theo giá trị tăng dần là:

\(S\in\left\{\frac{-1}{2};-1;\frac{-85}{2};46\right\}\)