Question

Doua multimi A si B au acelasi numar de elemente , numere naturale consecutive. Gasiti cele doua multimi daca suma elementelor celor doua multimi este 170, iar suma elementelor din multimea A intersectat cu Beste 17.

vreau rezolvarea scrisa va rog.

Answer 1

Fie k nr natural.
Avem cazul 1 A intersectat cu B ={17}
cazul 2 A intersectat cu B are 2 elemente k,k+1 deci 2k+1=17 deci k=8 A intersectat cu B{8,9}
cazul 3 A intersectat cu B are 3 elemente k,k+1,k+2=>3k+3=17 imposibil
cazul 4 A intersectat cu B are 4 elemente k,k+1,k+2,k+3=>4k+6=17 imposibil
cazul 5 A intersectat cu B are 5 elemente 5k+10=17 imposibil
cazul 6 A intersectat cu B are 6 elemente deci 6k+15=17 imposibil

Deci A intersectat cu B={17}sau{8,9}

daca A={16,17}si B={17,18}
17+17+16+18=68
daca A={15,16,17}si B={17,18,19}
68+15+19=102
daca A={14,15,16,17}si B={17,18,19,20}
102+14+20=136

daca A={13,14,15,16,17}si B={17,18,19,20,21}
136+13+21=170 solutia noastra.

cazul II

A={1,2,3,4,5,6,7,8,9} si B={8,9,10,11,12,13,14,15,16}
45+108=153

daca A={0,1,2,3,4,5,6,7,8,9} si B={8,9,10,11,12,13,14,15,16,17}
153+17=170 Solutia nr. 2