Răspuns:
[tex]\bf \textcolor{deeppink}{Solutie~(a,b,c)\in\{(2,3,13);(2,7,11); (2,19,5);(2,23,3)\}}[/tex]
Salutare!
Numerele prime sunt acele numere care au exact doi divizori, numărul 1 și numărul în cauză
Câteva numere prime: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc. ......
a, b, c fiind numere prime ele pot lua una din valorile de mai sus
[tex]\bf a+2b+4c=60[/tex]
↓ ↓ ↓
par par par ⇒ a = par
a = prim ⇒ a = 2
[tex]\bf 2+2b+4c=60[/tex]
[tex]\bf 2b+4c=60-2[/tex]
[tex]\bf 2b+4c=58~~\Big|:2[/tex]
[tex]\bf b+2c=29[/tex]
[tex]\bf 1)~Daca~\underline{b = 2}\implies 2+7c = 29\implies 2c= 27\implies c\notin\mathbb{N}[/tex]
[tex]\bf 2)~Daca~\underline{b = 3}\implies 3+2c = 29\implies 2c= 26\implies \underline{c=13}[/tex]
[tex]\bf 3)~Daca~\underline{b = 5}\implies 5+2c = 29\implies 2c= 24\implies c=12~nu~convine[/tex]
[tex]\bf4)~Daca~\underline{b = 7}\implies 7+2c = 29\implies 2c= 22\implies \underline{c=11}[/tex]
[tex]\bf 5)~Daca~\underline{b = 11}\implies 11+2c = 29\implies 2c= 18\implies c=9~nu~convine[/tex]
[tex]\bf 6)~Daca~\underline{b = 13}\implies 13+2c = 29\implies 2c= 16\implies c=8~nu~convine[/tex]
[tex]\bf 7)~Daca~\underline{b = 17}\implies 17+2c = 29\implies 2c= 12\implies c=6~nu~convine[/tex]
[tex]\bf 8)~Daca~\underline{b = 19}\implies 19+2c = 29\implies 2c= 10\implies \underline{c=5}[/tex]
[tex]\bf 9)~Daca~\underline{b = 23}\implies 23+2c = 29\implies 2c= 6\implies \underline{c=3}[/tex]
[tex]\boxed{\boxed{\bf \color{deeppink}{Solutie~(a,b,c)\in\{(2,3,13);(2,7,11); (2,19,5);(2,23,3)\}}}}[/tex]
#copaceibrainly
