Question

d)18 supra 2n+1apartine lui Z
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Answer 1

Explicație pas cu pas:

$\frac{18}{2n+1}$∈Z⇒2n+1∈ D₁₈⇒2n+1∈{±1,±2,±3,±9,±18}

2n+1=1⇒2n=0⇒n=0

2n+1=(-1)⇒2n=-2⇒n=-1

2n+1=2⇒2n=1⇒n=$\frac{1}{2}$∉Z

2n+1=(-2)⇒2n=(-3)⇒n=(-$\frac{3}{2}$)∉Z

2n+1=3⇒2n=2⇒n=1

2n+1=(-3)⇒2n=(-4)⇒n=(-2)

2n+1=9⇒2n=8⇒n=4

2n+1=(-9)⇒2n=(-10)⇒n=(-5)

2n+1=18⇒2n=17⇒n=$\frac{17}{2}$∉Z

2n+1=(-18)⇒2n=(-19)⇒n=$\frac{-19}{2}$∉Z