2)
a. \(n+5⋮n-2\Rightarrow n-2+7⋮n-2\)
\(\Rightarrow7⋮n-2\Rightarrow n-2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow n\in\left\{-5;1;3;9\right\}\)
b. \(2n+1⋮n-5\Rightarrow2n-10+11⋮n-5\)
\(\Rightarrow11⋮n-5\Rightarrow n-5\inƯ\left(11\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow n\in\left\{-6;4;6;16\right\}\)
c. \(n^2+3n-13⋮n+3\)
\(\Rightarrow n.n+3n-13⋮n+3\)
\(\Rightarrow n.\left(n+3\right)-13⋮n+3\)
\(\Rightarrow-13⋮n+3\Rightarrow n+3\inƯ\left(-13\right)=\left\{\pm1;\pm13\right\}\)
\(\Rightarrow n\in\left\{-16;-4;-2;10\right\}\)
d. \(n^2+3⋮n-1\Rightarrow n^2-n+n+3⋮n-1\)
\(\Rightarrow n.\left(n-1\right)+\left(n-1\right)+4⋮n-1\)
\(\Rightarrow4⋮n-1\Rightarrow n-1\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)
\(\Rightarrow n\in\left\{-3;-1;0;2;3;5\right\}\)
Câu 1:
a: \(\Leftrightarrow x^2-3x+2x-6=5\)
\(\Leftrightarrow x^2-x-11=0\)
hay \(x\in\left\{\dfrac{1+3\sqrt{5}}{2};\dfrac{1-3\sqrt{5}}{2}\right\}\)
b: \(\Leftrightarrow\left(x+1;xy-1\right)\in\left\{\left(1;3\right);\left(3;1\right);\left(-1;-3\right);\left(-3;-1\right)\right\}\)
\(\Leftrightarrow\left(x,xy\right)\in\left\{\left(0;4\right);\left(2;2\right);\left(-2;-2\right);\left(-4;0\right)\right\}\)
\(\Leftrightarrow\left(x,y\right)\in\left\{\left(2;1\right);\left(-2;1\right);\left(-4;0\right)\right\}\)
c: \(\Leftrightarrow\left(x-3;2y+1\right)\in\left\{\left(1;7\right);\left(7;1\right);\left(-1;-7\right);\left(-7;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(4;3\right);\left(10;0\right);\left(2;-4\right);\left(-4;-1\right)\right\}\)
