Question

Se dau multimile: A={x apartine IN / 6 supra x+2 apartine IN} si B={x apartine IN / 15 supra 2x+1 apartine IN} .   VA ROOOOOOG!!!!!!!!!!! REPEDE!!!!!!!!!!

Answer 1

A={x∈N/$\frac{6}{x+2}$∈N}
$\frac{6}{x+2}$∈N ⇒x+2 | 6 ⇒ x+2∈D₆ (divizorii naturali ai lui 6)
D₆={1,2,3,6} vom analiza 4 cazuri
1.x+2=1⇒x=-1 (nu analizam acest caz deoarece x∈Z)
2.x+2=2⇒x=0
3.x+2=3⇒x=1
4.x+2=6⇒x=4 deci A={0;1;4}
B={x∈N/$\frac{15}{2x+1}$∈N}
$\frac{15}{2x+1}$∈N⇒ 2x+1 | 15 ⇔ 2x+1∈D₁₅ 
D₁₅={1,3,5,15} 
1.2x+1=1⇒x=0
2.2x+1=3⇒x=1
3.2x+1=5⇒x=2
4.2x+1=15⇒x=7 deci B={0;1;2;7}