Question

Ajutati-ma va rog cu acest ex din imagine

Answer 1

var 2)  (12n+1)/(9n+4) eZ 
9n+4  I (divide) 12n+1  => 9n+4 I 9(12n+1)  =.> 9n+4 I 108n +9
9n+4  I                9n+4 => 9n+4 I 12(9n+4)  => 9n+4 I 108n +48
9n+4 I (108n+9) -(108n +48) 
9n+4 I 108n +9-108n -48
9n+4 I - 39

9n+4 = -39  => n=-43/9  nu apartine lui Z
9n+4 =-13  => n=-17/9  nu apartine lui Z
9n+4 =-3  => n=-7/9   nu apartine lui Z
9n+4 =-1  => n=-5/9  nu apartine lui Z
9n+4 =1 => n=-3/9 =-1/3  nu apartine lui Z
9n+4 =3 => n= -1/9  nu apartine lui Z
9n+4 =13 => n=9/9 =1
9n+4 =39 => n=35/9  nu apartine lui Z
Deci n = 1


var 1)  Tie n numere intregi:
(n^2 -3n+2) /(2n+1)  apartine lui Z
2n+1 I n^2 -3n+2  => 2n+1 I 2(n^2-3n+2) => 2n+1 I 2n^2-6n+4
2n+1 I 2n+1 => 2n+1 I n(2n+1) => 2n+1 I 2n^2 +n
2n+1 I (2n^2 -6n+4 ) -(2n^2 +n)  
2n+1 I 2n^2 -6n+4-2n^2-n
2n+1 I -7n+4
La fel : 
2n+1 I -7n+4  => 2n+1 I 2(-7n+4) => 2n+1 I -14n +8
2n+1 I 2n+1 => 2n+1 I 7(2n+1) => 2n+1 I 14n +7
2n+1 I (-14n+8) +(14n+7) 
2n+1 I -14n+8+14n+7 
2n+1 I 15  cu n apartine lui Z 

2n+1 =-15 => n = -8
2n+1 =-5 => n= -3
2n+1 =-3 => n= -2
2n+1 =-1 => n=-1 
2n+1 =1 => n=0
2n+1 =3 => n=1
2n+1 =5 => n=2
2n+1 =15 => n=7