Question

Aflati nr. x si y pentru care fractia 12 supra (x-1)(y-1) este echiunitara


COROANAAA

Answer 1

nu ai specificat dfin ce multime sunt numerele
 am lucrat inN, sa fie mai scurt

Answer 2

$\dfrac{12}{(x-1)(y-1)} \rightarrow fractie echiunitara \\ \\ \Rightarrow (x-1)(y-1) = 12 \\ \\ \bullet x-1 \in D_{12}^+ \Rightarrow x-1\in \Big\{1,2,3,4,6,12\Big\} \\ \\ \bullet y-1 \in D_{12}^+ \Rightarrow y-1\in \Big\{1,2,3,4,6,12\Big\} \\ \\ Dar, (x-1)(y-1) = 12 \\ \\x-1\in \Big\{1,2,3,4,6,12\Big\} si y-1 \in \Big\{12,6,4,3,2,1\Big\} \\ (in aceasta ordine) \\ Adunam cu 1 in ambele relatii \Rightarrow$

$\Rightarrow x\in \Big\{2,3,4,5,7,13\Big\} si y \in\Big\{13,7,5,4,3,2\Big\} \\ \\ Le grupam in ordinea pozitiilor:\\ \\ \Rightarrow (x,y) = \Big\{(2, 13); (3,7); (4,5); (5,4); (7,3);(13,2)\Big\}$