Question

Aflati numerele prime a, b, c care verifica simultan relatiile: c – ab = 15 si c – a^2 = 49.

Answer 1

$c-ab=15 \ \ =\ \textgreater \ c=15+ab \\\\ c-a^2=49 \ \ =\ \textgreater \ c=49+a^2 \\\\\\ 15+ab=49+a^2 \\\\ ab-a^2=49-15 \\\\ a(b-a)=34 \\\\ \hbox{Divizorii numarului 34 sunt --- 1;2;17;34} \\\\ \hbox{Numerele a,b,c sunt numere prime, iar cel mai mic nr. prim este 2} \\\\\\ \hbox{Se ia pe cazuri} \\\\\\ 1) a=2 \\\\ 2(b-2)=34 \\\\ b-2=17 \\\\ b=19 \\\\\\ c=15+2*19 <span>[tex]c=15+38 \\\\ c=53 \\\\\\ 2)a=17 \\\\ 17(b-17)=34 \\\\ b-17=2 \\\\ b=19 \\\\\\ c=15+17*19 \\\\ c= 15+323 \\\\ c=338 -nu \ este \ nr. \ prim \\\\ \hbox{Cade varianta 2, deci solutiile finale sunt: a=2; b=19 ; c=53}$ [/tex]