Question

Determinati numerele abc , pentru care are loc egalitatea : abc = 3cba + a + b +c
Ajutor!!! Dau coroana!

Answer 1

abc=100a+10b+c

cba=100c+10b+a

100a+10b+c= 3(100c+10b+a)+a+b+c

100a+10b = 300c+30b+3a+a+b

96a=300c+21b

a,b,c pot fi 1-9 (rezolvam prin înercari)

a = 8, c=2, b=8

96·8=300·2+21·8

768 = 600+168

a=8, b=8, c=2

abc=882, cba=288

V: 3·288+8+8+2=864+18=882=abc