Question

Exercitiul 16 !! 20 de puncte !!!

Answer 1

x+3 | 36 => x+3 apartine {1,36,2,18,3,12,4,9,6} => x apartine {-2,33,-115,9,1,6,3}
A= {33,15,9,1,6,3}
2x+1 | 45 => 2x+1 apartine {1,45,3,15,5,9} => 2x apartine {0,44,2,14,4,8} => x apartine {0,22,1,7,2,4}
B={22,1,7,2,4}
8 | x+5 => x+5 divizibil cu 8 => x+5 apartine {8,16,24,32,40,...} =? x apartine {3,11,19,27,35,...} x<=27
C={3,11,19}
15/(2x+1) apartine N => 2x+1 | 15 => 2x+1 apartine {1,15,3,5} => 2x apartine {0,14,2,4} => x apartine {0,7,1,2}
D={0,7,1,2}
21/(2x+3) apartine Z => 2x+3 | 21 => 2x+3 apartine {+/-1,+/-21,+/-3,+/-7} => 2x apartine {-2,18,0,4,-4,-25,-6,-10} => x apartine {-1,9,0,2,-2,-5,-3,-5}
E={-1,9,0,2,-2,-5,-3,-5}
(2x+5)/(x-1) apartine N => x-1 | 2x+5; x-1 | x-1 => x-1 | 4 => x-1 apartine {1,4,2} => x apartine {2,5,3}
F={2,5,3}
(3x+11)/(x+2) apartine Z => x+2 | 3x+11; x+2 | 3x+6 => x+2 | 5 => x+2 apartine {+/-1,+/-5} => x apartine {-1,3,-3,-7}
G={-1,3,-3,-7}
(3x+9)/(2x-3) apartine Z => 3x+9 | 2x-3; 3x+9 | 3x+9 => 3x+9 | x+12; 3(x+1) | x+12; 3(x+1) divide 3; 12 divide 3 => x divide 3 => x apartine {+/-0,+/-3+/-6,+/-9,+/-12+/-15+/-18,+/-21,...}
Sper ca te-am ajutat!