Doryanna
3

# aflați elementele următoarelor mulțimi: A={x€N|8/x. €N} B={x€N|12/x+1€ N} C={x€N|21/2x-1 € N} D={x€N|x+10/x+2 €N} E={x€N|2x+11/x+2 €N} F={x€N|3x+15/2x+3 €N} plzzz. Dau coroană. Nu toate câte puteți.

(2) Răspunsuri
zelenciuc

Deci pt inceput trebuie sa stii ca la toate multimile de mai sus au toate elementele cu nr naturale si trebuie sa respecte impartirea respectiva A = (0,1,2,4,8)  ex: 8/1 = 8; 8/2=4. B = (0,1,2,3,5,11) C = (1,2,4,11) D = (0,2,6) E = (5) F = (0,2,9)

laurall1

B={x€N|12/x+1€ N} $\it \dfrac{12}{x+1} \in\mathbb{N} \Rightarrow x+1|12 \Rightarrow x+1\in D_{12} \Rightarrow x+1 \in \{1,2, 3, 4, 6, 12\}|_{-1} \\\;\\ \\\;\\ \Rightarrow x \in \{0,\ 1,\ 2,\ 3,\ 5,\ 11\}$ B = {0,  1,  2,  3,  5,  11} ____________________________________________ E={x€N|2x+11/x+2 €N} $\it \dfrac{2x+11}{x+2} \in \mathbb{N} \Rightarrow x+2|2x+11 \ \ \ \ (1) \\\;\\ \\\;\\ Dar,\ \ x+2|x+2 \Rightarrow x+2| 2(x+2) \Rightarrow x+2| 2x+4 \ \ \ \ (2) \\\;\\ \\\;\\ (1),\ (2) \Rightarrow x+2| 2x+11-2x-4 \Rightarrow x+2| 7 \Rightarrow x+2\in\{1,7\} |_{-2}$ $\it \Rightarrow x \in \{-1,\ 5\} \\\;\\ Dar,\ x\in \mathbb{N}, \ deci\ \ x=7. \\\;\\ E=\{5\}$