Question

determina numerele naturale a,b, daca (a,b) =8 si axb =768.

Answer 1

a·b=768;
⇒a=8x;
⇒b=8y;
⇒8x·8y=768⇒64·x·y=768⇒x·y=12;
⇒x,y∈[[1,12],[2,6],[3,4],[4,3],[6,2],[12,1]⇒3·2=6 variante de raspuns;
⇒a,b∈[[8,96],[12,48],[24,32],[32,24],[48,12],[96,8]];

Answer 2

fie [tex] a_{1} [/tex] si$b_{1}$∈N cu($a_{1} , b_{1}$)=1
⇒a=$a_{1}$*8
   b=$b_{1}$*8
a*b=$a_{1} * b_{1}$*64
768=$a_{1} * b_{1}$*64
$a_{1} * b_{1}$=768/64
$a_{1} * b_{1}$=12=1*12=3*4=4*3=12*1(2*6 nu convine deoarece c.m.m.d.c. este 1)⇒$a_{1}$=1⇒a=1*8=8
                               $b_{1}$=12⇒b=12*8=96
$a_{1}$=3⇒a=3*8=24
$b_{1}$=4⇒b=4*8=32
si inversele a=96 si b=8
                    a=32 si b=24