Question

Determinati valorile intregi ale lui n pt care relatia de mai jos reprezinta propozitie adevărata 9n+16/3n+2

Answer 1

$\frac{9n+16}{3n+2}= \frac{9n+6+10}{3n+2} = \frac{9n+6}{3n+2}+ \frac{10}{3n+2} \\ \\ \frac{3(3n+2)}{3n+2}+ \frac{10}{3n+2} = \\ \\ 3+ \frac{10}{3n+2} =$
3n+2 apartine divizorilor lui 10 {+1, -1, +2, -2, +5, -5, +10, -10}

3n+2=1⇒3n=1-2⇒3n=-1⇒n =- 1/3 ∉N

3n+2=-1⇒3n=-1-2⇒3n=-3⇒n=-1 ∉N

3n+2=2⇒3n=2-2⇒n = 0 ∈N

3n+2=-2⇒3n=-2-2⇒3n=-4⇒n = - 4/3 ∉N

3n+2=5⇒3n=5-2⇒3n=3⇒n =1∈ N

3n+2=-5⇒3n=-5-2⇒3n=-7/3⇒n = -7/3∉N

3n+2=-10⇒3n=-10-2⇒3n=-12⇒n = -4 ∉N

3n+2=10⇒3n=10-2⇒3n=8⇒n = 8/3∉ N

deci valorile pe care le poate lua n sunt n=1∈N,  si n=0∈N