Question

Determinati x ∈ N pentru care :
a) 6 supra x-1 ∈ N
b) 14 supra 3x-1 ∈ N
c) 21 supra 2x+1 ∈ N

Answer 1

6/(x-1)∈N trebuiesc determinati divizorii lui 6,d6={-6,-3,-2,-1,1,2,3,6}
x-1=6 ,x=7
x-1=3 ,x=4
x-1=2,x=3
x-1=1,x=2
x-1=-1,x=0
x={0,2,3,4,7}

b) 14/(3x-1)
3x-1=14,x=5
3x-1=7,x∉N
3x-1=1,x∉N
3x-1=-1 ,x=0
x={0,5}

c)21/(2x+1)
2x+1=1,x=0
2x+1=3,x=1
2x+1=7,x=3
2x+1=14,x∉N
x={0,1,3}