Question

Impartind doua numere naturale , obtinem catul 14 si restul 3 . Daca impartim suma lor la diferenta lor , obtinem catul si rest 26 . Aflati numerele .

Answer 1

a : b = 14 rest 3
a = 14b + 3
(a + b) : (a - b) = 26 rest 26
a + b = 26 (a - b) + 26
a + b = 26a - 26b + 26
- 26a + a + b + 26b = 26
- 25a + 27b = 26
- 25 * (14b + 3) + 27b = 26
- 350b - 75 + 27b = 26
- 323b = 75 + 26
- 323 b = 101
b = 101/323
a = 14 * 101/323 + 3 
323a = 1414 + 969
a = 2383/323