Question

Aflati nr.ab in baza zece,daca (ab-in baza zece +ba-in baza zece)/(ab-in baza zece-ba-in baza zece)=
11
VA ROG FRUMOS!!!

Answer 1

ab+ba/ab-ba = 11
10a+b+10b+a / 10a+b-10b-a = 11
11a+11b / 9a-10b+b = 11
11a+11b / 9a-(10b-b) = 11
11a+11b / 9a-9b = 11
11(a+b) / 9(a-b) = 11
11(a+b) / 11 = 9(a-b)
a+b = 9(a-b)
a+b = 9a-9b
a+b+9b = 9a
a+10b = 9a
10b = 9a-a
10b = 8a
5b = 4a
[5, 4] = 20
Daca 5b=4a=20, atunci a=5 si b=4, singura solutie pentru care a si b sunt cifre
ab=54