b) Din(a,b)=7, obtinem a=7x,b=7y si (x,y)=1.Relatia a·b=294 devine 7x·7y=294 si impartind prin 49 termenii egalitatii obtinem x·y=294:49=6. Dupa valorile lui y studiem cazurile :
1.y=1⇒x=6⇒a=7·6=42;b=7·1=7 rezulta perechea (42,7)
2.y=2⇒x=3⇒a=7·3=21;b=7·2=14 rezulta perechea (21,14)
3.y=3⇒x=2⇒a=7·2=14;b=7·3=21 rezulta perechea (14,21)
4.y=6⇒x=1⇒a=7·1=7;b=7·6=42 rezulta perechea (7,42)
18 a) (a,b)=750:150=5;a=5x;b=5y si (x,y)=1.Relatia a·b = 795 devine 5x·5y=750si impartind prin 25 termenii egalitatii obtinem x·y=750:25=30.Dupa valorile lui y studiem cazurile:
1.y=1⇒x=30⇒a=5·30=150;b=5·1=5 rezulta perechea (150,5)
2.y=2⇒x=15⇒a=5·15=75;b=5·2=10 rezulta perechea (75,10)
3.y=3⇒x=10⇒a=5·10=50;b=5·3=15 rezulta perechea (50,15)
4.y=5⇒x=6⇒a=5·6=30;b=5·5=25 rezulta perechea (30,25)
5.y=6⇒x=5⇒a=5·5=25;b=5·6=30 rezulta perechea (35,30)
6.y=10⇒x=3⇒a=5·3=15;b=5·10=50 rezulta perechea (15,50)
7.y=15⇒x=2⇒a=5·2=10;b=5·15=75 rezulta perechea (10,75)
8.y=30⇒x=1⇒=a=5·1=5;b=5·30=150 rezulta perechea (5,150)
b) (a,b)=864:72=12;a=12x;b=12y si (x,y)=1.Relatia a·b = 864 devine 12x·12y=864si impartind prin 144(12·12) termenii egalitatii obtinem
x·y=864:144=6.Dupa valorile lui y studiem cazurile:
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)
