Question

Fie x=[ a(a + 1) ] totul cu bara deasupra, y = [ b(b+1) ] totul cu bara deasupra.. doua numere scrise in baza zece astfel in x+y = 112. Aflati multimea A= { (x,y) l (x,y) = 2 }

Answer 1

Scriem nr in baza zece
x= 10a+a+1=11a+1
b=10b+b+1=11b+1
x+y=112⇔11a+1+11b+1=112
11a+11b=112-2
11(a+b)=110
a+b=10
(a,b)=2
a=2;b=8
a=4;b=6
A={ (2;8); (8;2); (4;6); (6;4)}