Question

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

Answer 1

daca (a,b)=8 => a=x*8 si b=y* 8   ( cu x,y nr naturale) 
cum a*b=768 => inlocuim => x*8*y*8=768
x*y=12
acum cautam toate nr. naturale care inmultite dau 12
1. x=1 si y=12 => a=8 si b=96
2. x=2 si y=6 => a=16 si b=48
3. x=3 si y= 4 => a=24 si b=32
4. x=4 si y=3 => a=32 si b=24
5. x=6 si y=2 => a=48 si b=16
6. x=12 si y=1 => a=96 si  b=8

Answer 2

a=8x;
b=8y;
⇒a·b=768
⇒8·x·8·y=868
⇒64·x·y=768
⇒x·y=12;⇒x,y∈[[1,12],[2,6],[3,4],[4,3],[6,2],[12,1]];
⇒a,b∈[[8,96],[16,48],[24,32],[32,24],[48,16],[96,8]];