Question

Aflati numarul abc stiind ca a,b(c)+b,c(a)+c,a(b)=2,(2)
Va rooggggg

Answer 1

banuiesc ca toate numerele astea sunt cu bara deasupra, adica in baza 10
a,b(c)=(abc-ab)/90=(100a+10b+c-10a-b)/90=(90a+9b+c)/90
b,c(a)=(90b+9c+a)/90 (similar cu cel de sus)
c,a(b)=(90c+9a+b)/90
le adunam
2,(2)=(90a+90b+90c+9a+9b+9c+a+b+c)=100(a+b+c)/90=10(a+b+c)/9
2,(2)=(22-2)/9=20/9
egalam
10(a+b+c)/9=20/9
a+b+c=2
abc este un numar, deci cu bara deasupra(in baza 10)⇒a, b, c-cifre, a≠0
avem solutiile
abc∈{101, 110, 200}