Question

Determină numarul natural x , astfel încat 18 supra 2x+1 aparţine numerelor naturale nule.

Answer 1

18/(2x + 1) ∈ N
D18 = {1; 2; 3; 6; 9; 18} ⇒ 2x + 1 ∈ {1; 2; 3; 6; 9; 18}
2x + 1 ∈ {1; 2; 3; 6; 9; 18}/-1
2x ∈ {0; 1; 2; 5; 8; 17}/ ÷2
x ∈ {0; 1/2; 1; 3/2; 4; 17/2} Dar deoarece x ∈ N nu putem lua fractiile ⇒
⇒ x ∈ {0; 1; 4}.

Answer 2

$\frac{18}{2x+1}$  ∈ N
x ∈ N
D18 = {1; 2; 3; 6; 9; 18} ⇒ 2x + 1 ∈ {1; 2; 3; 6; 9; 18}

2x+1=18 ⇒ 2x=17 ⇒ x =$\frac{17}{2} =8,5$∉N

2x+1=9⇒ 2x= 8 ⇒ x=4 ∈ N

2x+1=2⇒ 2x=1 ⇒x=$\frac{1}{2} =0,5$ ∉ N

2x+1=1⇒ 2x=0 ⇒ x=0 ∈ N

2x+1=3⇒2x=2⇒x=1 ∈N

2x+1=6⇒2x=5⇒x=$\frac{5}{2} =2,5$ ∉ N

x ∈ { 0;1;4}