Răspuns:
Explicație pas cu pas:
a) 6/(x+1) ∈N x∈N
Numitorul trebuie sa fie unul din divizorii naturali ai naumaratorului.
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 ⇒x∈{0,1,2,5}
b)15/(2x-3)∈Z
D15={±1,±3,±5,±15} x∈N
2x-3=1 ⇒x=2 ok
2x-3=-1 x=1 ok
2x-3=3 x=3 ok
2x-3=-3 x=0 ok
2x-3=5 x=4 ok
2x-3=-5 x=-1 nu e natural
2x-3=15 x=9 ok
2x-3=-15 x=-6 nu e natural
x={0,1,2,3,4,9}
c)12/(4x-1) ∈N
D12={1,2,3,4,6,12}
4x-1=1 x=1/2 nu e natural
4x-1=2 x=3/4 nu e natural
4x-1=3 x=1 ok
4x-1=4 x=5/4 nu e natural
4x-1=6 x=7/6 nu e natural
4x-1=12 x=13/4
solutie unica x=1
d)28/(3x-2)∈Z
D28={±1,±2,±4,±7,±14,±28}
3x-2=1 x=1 ok
3x-2=-1 x=1/3 nu
3x-2=-2 x=0 ok
3x-2=2 x=4/3 nu
3x-2=4 x=2 ok
3x-2=-4 x=-2/3 nu
3x-2=7 x=3 ok
3x-2=-7 x=-5/3 nu
3x-2=14 x=4 ok
3x-2=-14 x=-16/3 nu
x={0,1,2, 3,4}
