Question

Vaa rog ma ajutati cu ex asta?

Answer 1

ab + cd = 47 → suma a doua numere

ba + dc = 173 → suma rasturnatelor celor doua numere

_______________________ → adun sumele

10 a + b + 10 c + d + 10 b + a + 10 d + c = 47 + 173

11 a + 11 b + 11 c + 11 d = 220

11 ( a + b + c + d ) = 220

a + b + c + d = 220 : 11

a + b + c + d = 20 → suma cifrelor celor doua numere si a rasturnatelor acestora

______________________

( ba + dc ) - ( ab + cd ) = 173 - 47

10 b + a + 10 d + c - 10 a - b - 10 c - d = 126

9 b + 9 d - 9 a - 9 c = 126

9 ( b + d - a - c ) = 126

b + d - a - c = 126 : 9

b + d - a - c = 14

_____________

( a + b + c + d ) - ( b + d - a - c ) = 20 - 14

a + b + c + d - b - d + a + c = 20 - 14

2 a + 2 c = 6

2 ( a + c ) = 6

a + c = 6 : 2

a + c = 3 ⇒ a + b + c + d = 20 ⇒ b + d = 17

a,b, c, d ≠ 0

Solutii: ( ab; cd) = ( 18; 29); ( 28; 19)

Verific:

18 + 29 = 29 + 18 = 47 → suma celor doua numere

81 + 92 = 92 + 81 = 173 → suma rasturnatelor celor doua numere