Question

verificati egalitatea (a·b) · [a·b] = a·b pentru fiecare pereche de numere indicata

a) a=12, b=20
b) a=27, b=36
c) a=18, b=36
d) a=46, b=72


vreau raspunsul repede

Answer 1

(a;b)•[a;b]=a•b

a)
12=2²•3
20=2²•5
-------------
(12;20)=2²=4
[12;20]=2²•3•5=4•3•5=3•20=60

(12;20)•[12;20]=12•20
4•60=12•20
240=240

b)
27=3³
36=2²•3²
-------------
(27;36)=3²=9
[27;36]=2²•3³=4•27=108

(27;36)•[27;36]=27•36
9•108=27•36
972=972

c)
18=2•3²
36=2²•3²
-------------
(18;36)=2•3²=2•9=18
[18;36]=2²•3²=4•9=36

(18;36)•[18;36]=18•36
18•36=18•36
648=648

d)
46=2•23
72=2³•3²
------------
(46;72)=2
[46;72]=2³•3²•23=8•9•23=1656

(46;72)•[46;72]=46•72
2•1656=46•72
3312=3312