Question

Determinati elemente urmatoarelor multimi: A={x apartine Z| 6/2x+1 apartine Z} B={x apartine Z| -8/3x-1 apartine Z}

Answer 1

A={x ∈ Z| 6/2x+1 ∈ Z}
Ca 6/2x+1 ∈ Z => consideram divizorii lui  6∈Z = 2x+1
$\left \{ {{2x+1=6} \atop {2x+1=-6}} \right. =\ \textgreater \ \left \{ {{x=5/2~~NU} \atop {X=-7/2~~NU}} \right.$
$\left \{ {{2x+1=3} \atop {2x+1=-3}} \right. =\ \textgreater \ \left \{ {{X=1} \atop {X=-2}} \right.$
$\left \{ {{2x+1=2} \atop {2x+1=-2}} \right. =\ \textgreater \ \left \{ {{X=1/2~~NU} \atop {X=-3/2~~NU}} \right.$
$\left \{ {{2x+1=1} \atop {2x+1=-1}} \right. =\ \textgreater \ \left \{ {{X=0} \atop {X=-1}} \right.$
=> A={-2,-1,0,1}

B={x ∈ Z| -8/3x-1 ∈ Z}
Ca -8/3x-1 ∈ Z => consideram divizorii l3x-1∈Z  = 2x+1
$\left \{ {{3x-1=8} \atop {3x-1=-8}} \right. =\ \textgreater \ \left \{ {{X=3} \atop {X=-7/3~~NU}} \right.$
$\left \{ {{3x-1=4} \atop {3x-1=-4}} \right. =\ \textgreater \ \left \{ {{X=5/3~~NU} \atop {X=-1}} \right.$
$\left \{ {{3x-1=2} \atop {3x-1=-2}} \right. =\ \textgreater \ \left \{ {{X=1} \atop {X=-1/3~~NU}} \right.$
$\left \{ {{3x-1=1} \atop {3x-1=-1}} \right. =\ \textgreater \ \left \{ {{X=2/3} \atop {X=0}} \right.$
B={-2,-1,0,1,3}