Răspuns :
18/2x+1∈N⇒2x+1∈D18
D18∈{1,2,3,6,9,18}
1. 2x+1=1
2x=1-1
2x=0
x=0:2=0
2. 2x+1=3
2x=3-1
2x=2
x=2:2=1
3. 2x+1=9
2x=9-1
2x=8
x=8:2=4
D18∈{1,2,3,6,9,18}
1. 2x+1=1
2x=1-1
2x=0
x=0:2=0
2. 2x+1=3
2x=3-1
2x=2
x=2:2=1
3. 2x+1=9
2x=9-1
2x=8
x=8:2=4
[tex] \frac{18}{2x+1}apartine~lui~N\\
18~trebuie~sa~se~imparta~exact~la~2x+1\\
18,se~imparte~exact~la:1,2,3,6,9,deci~2x+1=1,2,3,6,9.\\
=\ \textgreater \ 2x+1=1=\ \textgreater \ 2x=0=\ \textgreater \ x=0\\
2x+1=2=\ \textgreater \ 2x=1=\ \textgreater \ x=0,5\\
2x+1=3=2x=2=\ \textgreater \ x=1\\
2x+1=6=\ \textgreater \ 2x=5=\ \textgreater \ x=2,5\\
2x+1=9=\ \textgreater \ 2x=8=\ \textgreater \ x=4\\\\
Proba:2*0+1=1=\ \textgreater \ 18:1=18(corect)\\
2*0,5+1=1+1=2=\ \textgreater \ 18:2=9(corect)\\
2*1+1=3=\ \textgreater \ 18:3=6(corect)\\
2*2,5+1=5+1=6=\ \textgreater \ 18:6=3(corect)\\
2*4+1=9=\ \textgreater \ 18:9=2(corect)\\
[/tex]