Question

Perechile de nr (x,y ) stiind ca x supra 12 = 3 supra xy-x

Answer 1

x/12=3/xy-x
⇒x×xy-x×x=12×3
⇒x[xy-x]=36
⇒36=1×36 sau 36=2×18 sau 36=3×12 sau 36=4×9
36=6×6 sau 36=9×4 sau 36=12×3 sau 36=18×2 sau 36=36×1;
⇒x∈[1,2,3,4,6,9,12,18,36];
⇒xy-x=36 sau xy-x=18 sau xy-x=12 sau xy-x=9 sau xy-x=6 sau xy-x=4 sau xy-x=3 sau xy-x=2 sau xy-x=1;
⇒1×y-1=36⇔1y=37⇔y=37 sau 2×y-2=18⇔2y=20⇔y=10 sau 3×y-3=12⇔3y=15⇔y=5 sau 4×y-4=9⇔4y=13⇔y=3,25∉N sau 6×y-6=6⇔6y=12⇔y=2 sau 9×y-9=4⇔9y=13⇔y=1,[4]∉N sau 12×y-12=3⇔12y=15⇔y=1,25∉N sau 18×y-18=2⇔18y=20⇔y=1,[1]∉N sau 36×y-
36=1⇔36y=37⇔y=1,02[7]∉N;
⇒perechile de nr. sunt  x,y∈[[1,37],[2,10],[3,5],[6,2];