Question

Determinați numărul natural x daca:
a)x+1|24
b)2x+1|35
c)2x-3|42
d)3x-1|40
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Answer 1

a)x+1|24⇒x+1∈D₂₄⇒x+1∈{1,2,3,4,6,8,12,24}
1 caz
x+1=1|-1
x=0∈N
2 caz
x+1=2|-1
x=1∈N
3 caz
x+1=3|-1
x=2∈N
4 caz
x+1=4|-1
x=3∈N
5 caz
x+1=6|-1
x=5∈N
6 caz
x+1=8|-1
x=7∈N
7 caz
x+1=12|-1
x=11∈N
8 caz
x+1=24|-1
x=23∈N
x∈{1,2,3,5,7,11,23}
b)2x+1|35⇒2x+1∈D₃₅⇒2x+1∈{1,5,7,35}
ex
2x+1=1|-1
2x=0|:2∉N
2x+1=5|-1
2x=4|:2
x=2∈N
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