Question

55 puncte!
Explicați-mi cum se rezolvă subpunctul f, pas cu pas vă rog... ​

Answer 1

$\dfrac{4n+11}{2n+3} = \dfrac{4n+6+5}{2n+3} = \dfrac{2(2n+3)+5}{2n+3} =\\ \\ =\dfrac{2(2n+3)}{2n+3} +\dfrac{5}{2n+3} = 2+\dfrac{5}{2n+3}\in \mathbb{N}\\ \\\\\Rightarrow 2n+3\,\,\big|\,\, 5 \Rightarrow 2n+3\in D_{5} \Rightarrow 2n+3\in \big\{-5,-1,1,5\big\}\Big|-3\\ \Rightarrow 2n \in \{-5-3,-1-3,1-3,5-3\big\} \Rightarrow 2n\in \big\{-8,-4,-2,2\big\}\Big|:2\\ \Rightarrow n \in \left\{-\frac{8}{2},-\frac{4}{2},-\frac{2}{2},\frac{2}{2}\right\} \Rightarrow n\in \big\{-4,-2,-1,1\big\}$

$\\\text{Observam ca pentru }n = -2, \,\,\text{expresia este }-3 \text{ (nu verifica).}\\ \\ \Rightarrow \boxed{n\in \Big\{-4,-1,1\Big\}}$