Question

Determinati nr prime a b si c diferite doua cate doua stiind ca: a) a+2b+4c=36. b) 3a+16=54 urgenttttttt ! Multumesc !!!

Answer 1

 [tex]a).\;2b\vdots2\;\;;\;\;4c\vdots2\;\;si\;\;36\vdots2\;\;\rightarrow\;a\,\vdots\,2\rightarrow\,a=2 \\ .\;\;\;\;inseamn\u{a}\;c\u{a}\;\;2b+4c=36-2=34 \;\;|_{:2}\\ .\;\;\;\;b+2c=17\;\;\rightarrow 17=3+2*deci\;\;\fbox{a=2\;;\;b=3\;si\;c=7}\;;\\ b).\;3a+16b=54\;|_{:3}\rightarrow\;16b\,\vdots\,3\;\rightarrow\;\fbox{b=3}\;;\\ .\;\;\;\;atunci,\;3a+16*3=54\Leftrightarrow\;3a=54-48=6\;\\ .\;\;\;\;adica:\;3a=6\;\;deci\;\fbox{a=2}. [/tex]

Answer 2

a. a+2b+4c=36⇒36-numar; 4c-numar ,c∈N⇒2b-numar par ,b∈N⇒a-numar par⇒a-numar prim;
⇒a=2;
⇒2+2b+4c=36
⇒2b+4c=34⇒4c<34⇒c=[2,3,5,7]⇒patru variante;
⇒c=2⇒2b+8=34⇒2b=26⇒b=13⇒numar prim;
⇒c=3⇒2b+12=34⇒2b=22⇒b=11⇒numar prim;
⇒c=5⇒2b+20=34⇒2b=14⇒b=7⇒numar prim;
⇒c=7⇒2b+28=34⇒2b=6⇒b=3⇒numar prim;
b=[3,7,11,13]⇒patru variante;⇒a≠b≠c⇒a=2⇒c=5⇒b=7;
b. 3a+16b=54⇒54-numar par; 16b-numar par ,b∈N; 3a-numar par⇒a=2⇒numar prim par;
⇒6+16b=54⇒16b=48⇒b=3⇒numar prim impar;