Question

Va rog sa ma ajutati!! Maine am test si nu am inteles cum se face exercitiul asta!!!
Determinati elementele multimilor:
A={x apartine N* |x+3| 36};
B={x apartine N*|2x+1| 45};
C={x apartine N |x mai mic sau egal cu 27;8|x+5};
D={x apartine N |15 pe2x+1 apartine N};
E={x apartine Z |21 pe 2x+3 apatine Z};
F={x apartine N | 3x+9 pe x+1 apartine N};
G={x apartine Z \ {-2} | 3x+11 pe x+2 apartine Z}
H={x apartine Z | 3x+9 pe 2x-3 apartine Z}

Answer 1

x+3|36
D36=1,2,3,4,6,9,12,18,36
x+3=1 nu , x∈N*
x+3=2 nu, n∈N*
x+3=3 nu, n∈N*
x+3=4, x=1
x+3=6, x=3
x+3=9, x=6
x+3=12, x=9
x+3=18, x=15
x+3=36, x=33
A={1,3,6,9,15,33}

D45=1,3,5,9,15,45
2x+1=1 nu
2x+1=3, x=1
2x+1=6, x=5/2 nu
2x+1=9, x=4
2x+1=15, x=7
2x+1=45, x=22
B={1,4,7,22}

alegem doar x+5=m8≤27, m∈N*, x∈N

x+1=8, x=7
x+1=16, x=15
x+1=24, x=23
C={7,15,23}

D15=1,3,5,15
2x+1=1,x=0
2x+1=3, x=1
2x+1=5, x=2
2x+1=15, x=7
D={0,1,2,7}

DI21=-21, -7, -3, -1, 1, 3, 7, 21
2x+3=-21, 2x=-24, x=-12
2x+3=-7, x=-5
2x+3=-3, x=-3
2x+3=-1, x=-2
2x+3=1, x=-1
2x+3=3, x=0
2x+3=7, x=2
2x+3=21, x=9
E={-5,-3, -2, -1, 0, 2, 9}

(3x+9)/(x+1)=(3x+3+6)/(x+1)=3+6/(x+1)

D6=1,2,3,6
x+1=1, x=0
x+1=2, x=1
x+1=3, x=2
x+1=6, x=5
F={0, 1, 2, 5}

(3x+11)/(x+2)=(3x+6+5)/(x+2)=3+5/(x+2)
DI5=-5, -1, 1, 5 (DI5 divizorii intregi ai lui 5)
x+2=-5, x=-7
x+2=-1, x=-3
x+2=1, x=-1
x+2=5, x=3
G={-7, -3, -1, 3}

(3x+9)/(2x-3)=1/2 x (6x+18)/(2x+3)= 1/2 x [3+27/(2x+3)]
DI27=-27, -9, -3, -1, 1, 3, 9, 27
2x+3=-27, x=-15
2x+3=-9, x=-6
2x+3=-3, x=-3
2x+3=-1, x=-2
2x+3=1, x=-1
2x+3=3, x=0
2x+3=9, x=3
2x+3=27, x=12
H={-15, -6, -3, -2, 0, 3, 12}