Question

Determinati valorile intregi ale lui a pentru care E(a) ia valori intregi, ( E(a)=3/x-3 )

Answer 1

3/x-3 rezlta x-3 apartine multiplii lui3=(3,-3,9,-9 ....)
1).x-3=3,x=6
2)x-3=-3,x=0
3)x-3=9,x=12
4)x-3=-9,x=-6
etc.multimea multiplilor unui nr este infinita

Answer 2

 $E(a)=\frac{3}{x-3}\;\in\;\mathbb{Z}\;dac\u{a}\;\; x-3=D_3=\{\pm1\;;\;\pm3\}$
[tex]\Downarrow\;\\ x-3=-1\;\;...\;\;x=2\;;\\ x-3=\;\;1\;\;\;...\;\;x=4\;;\\ x-3=-3\;\;...\;\;x=0\;;\\ x-3=\;\;3\;\;\;...\;\;x=6\;;\\[/tex]