Question

Verificati egalitatile urmatoare:
(6,15) × [6,15]=6×15;
(18,24)×[18,24]=18,24;
(8,20)×[8,20]=8,20;
(28,42)×[28,42]=28,42.
b)Daca (a,b)=6 si [a,b]=72, aflati a × b,
c)Daca (a,b)=12 si a × b =864, aflati [a,b].
d)Daca [a,b]=96 si a × b=3072,aflati (a,b).
Daca [a,b] =432, (a,b)=12 si a =48,aflati b.
Va rog frumos!

Answer 1

6=2×3
15=3×5
cmmdc=3
cmmmc=2×3×5=30
3x30=90
(6,15) × [6,15]=6×15=90    deci adevarat

18=2×3²
24=2³×3
cmmdc=2×3=6
cmmmc=2³×3²=72
6x72=432
(18,24) × [18,24]=18,24    deci fals

8=2³
20=2²×5
cmmdc=2²=4
cmmmc=2³×5=40
4x40=160
(8,20) × [8,20]=8,20    deci fals

28=2²×7
42=2×3×7
cmmdc=2×7=14
cmmmc=2²×3×7=84
14x84=1176
(28,42) × [28,42]=28,42    deci fals


b)Daca (a,b)=6 si [a,b]=72
 a × b =6×72=432

c)Daca (a,b)=12 si a × b =864
[a,b]=864:12=72

d)Daca [a,b]=96 si a × b=3072
 (a,b)=3072:96=32

Daca [a,b] =432, (a,b)=12 si a =48,aflati b.
a·b=432·12=5184
b=5184:48=108