Question

Aflati numerele a, b, c, (in baza 10) de forma ab+bc+ca=abc

Answer 1

__    __    __    ___

ab + bc + ca = abc   ⇔  10a+b+10b+c+10c+a=100a+10b+c

                            11a+11b+11c = 100a+10b+c

                                                                                       __

                  89a - 10c-b = 0  ⇔  89a=10c+b ⇔ 89×a =  cb

                                                                                ↓       ↓

                                                                                        __

                                                                             a=1 si  cb=89

                                        ___

R: a=1; b=9 si c=8  deci  abc = 198 .