Question

va rog!

determinati nr. nat a,b care indeplinesc simultan conditiile:
(a,b)=18,7a+3b=1512

Answer 1

a=x*18; b=y*18
7*x*18+3*y*18=1512 =>18*(7x+3y)=1512
7x+3y=84 => 7x<84 => x<12
3y=84-7x=> y=(84-7x)/3=84/3-7x/3=28-7x/3
28-7x/3 trebuie sa fie un numar natural => x/3 trebuie sa fie numar natural
pt. x=3 => y=28-7=21 => a=3*18=54; b=21*18=378
pt x=6 => y=28-7*2=14 => a=6*18; b=14*18
pt x=9 => y=28-7*3=7 => a=9*18; b=7*18