Question

Fie a,b €\Z. a-2/3=1/b+3,atunci perechile (a,b)sunt

Answer 1

"Fie a,b €\Z. a-2/3=1/b+3,atunci perechile (a,b)sunt"

 Fie a, b ∈ ℤ,  (a-2)/3 = 1/(b+3), atunci perechile (a, b) sunt ...

[tex]\it \dfrac{a-2}{3} =\dfrac{1}{b+3} \Rightarrow (a-2)(b+3) = 3 = -3\cdot(-1) = -1\cdot(-3) = \\ \\ \\ = 1\cdot3 = 3\cdot1 \\ \\ \\ a-2 \in \{ -3,\ -1,\ 1,\ 3\} |_{+2} \Rightarrow a\in \{-1, \ 1,\ 3,\ 5\} [/tex]

[tex]\it b+3 \in\{-1,\ -3,\ 3,\ 1\}|_{-3} \Rightarrow b\in \{-4, \ -6,\ 0, \ -2\} \\ \\ (a,\ b) \in \{ (-1,\ -4),\ (1,\ -6),\ (3,\ 0), \ (5,\ -2)\}[/tex]