Question

(a,b)=12 5a+2b=348 va rog cine ma poate ajuta

Answer 1

a=12m
b=12n
m,n∈N

5a+2b=60m+24n
60m+24n=348 ....:4
15m+6n=87
6n=87-15m

n= (87-15m)/6 ∈N

pt m=0,2;4, 6, 2k numaratorul n este impar, nu se imparte la 6, n∉N
deci nu le vom incerca

pt m=1, obtinem n=72:6=12
ptm=3, obtinem n=42:6=7

ptn=5 obtinem n=12:6=2
 ptn≥7, obtinem n mai mic decat 0
deci raman doar
(n,m) ∈multimii (1,12) (3;7) (5,2)

deci (a,b)∈multimii (12,144), (36;84);(60;24)  care verifica relatia