Question

Aflati 3 numere naturale a,b,c daca:a·b=144 . b·c=240 . a·c=60

Answer 1

a*b*b*c*a*c=144*240*60
a^2 * b^2 * c^2 = 144*240*60
(a*b*c)^2 = 12^2 * 240 * 60
(a*b*c)^2 = 12^2 * 4 * 60 * 60
(a*b*c)^2 = 12^2 * 2^2 * 60^2
(a*b*c)^2 = (12*2*60)^2
a*b*c = 12*2*60
a*b*c=1440
a = a*b*c : b*c = 1440:240 = 6
b = a*b*c : a*c = 1440:60 = 24
c = a*b*c : a*b = 1440:144 = 10