Question

feterminati numerele a si b in fiecare caz [a,b]=72 si axb=864

Answer 1

[a,b]=72 si axb=864
se utilizeaza proprietatea:[a,b] x (a,b)=a x b
deci (a,b)=(a×b)/[a,b]

(a,b)=864/72=12

a=12x;b=12y si (x,y)=1
Relatia a·b = 864 devine 12x·12y=864
⇒xy=864:144
⇒xy=6
vor da produsul = 6 numerele (1,6) sau (2,3)

1.y=1⇒x=6⇒a=12·6=72;b=12·1=12 rezulta perechea (72,12)
2.y=2⇒x=3⇒a=12·3=36;b=12·2=24 rezulta perechea (36,24)
3.y=3⇒x=2⇒a=12·2=24;b=12·3=36 rezulta perechea (24,36)
4.y=6⇒x=1⇒a=12·1=12;b=12·6=72 rezulta perechea (12,72)