Question

Aflati nr prime a,b,c stiind a+2b+4c=60 pls dau coroana inima si 5 stele​

Answer 1

Răspuns: $\bf (a,b,c)\in\{(2,3,13);(2,7,11); (2,19,5);(2,23,3)\}$

Explicație pas cu pas:

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

$\bf a+2b+4c=60$

      ↓       ↓       ↓

    par     par    par   ⇒ a = par

                                     a = prim    ⇒ a  = 2

$\bf 2+2b+4c=60$

$\bf 2b+4c=60-2$

$\bf 2b+4c=58~~\Big|:2$

$\bf b+2c=29$

$\bf 1)~Daca~\underline{b = 2}\implies 2+7c = 29\implies 2c= 27\implies c\notin\mathbb{N}$

$\bf 2)~Daca~\underline{b = 3}\implies 3+2c = 29\implies 2c= 26\implies \underline{c=13}$

$\bf 3)~Daca~\underline{b = 5}\implies 5+2c = 29\implies 2c= 24\implies \underline{c=12}~nu~convine$

$\bf 4)~Daca~\underline{b = 7}\implies 7+2c = 29\implies 2c= 22\implies \underline{c=11}$

$\bf 5)~Daca~\underline{b = 11}\implies 11+2c = 29\implies 2c= 18\implies \underline{c=9}~nu~convine$

$\bf 6)~Daca~\underline{b = 13}\implies 13+2c = 29\implies 2c= 16\implies \underline{c=8}~nu~convine$

$\bf 7)~Daca~\underline{b = 17}\implies 17+2c = 29\implies 2c= 12\implies \underline{c=6}~nu~convine$

$\bf 8)~Daca~\underline{b = 19}\implies 19+2c = 29\implies 2c= 10\implies \underline{c=5}$

$\bf 9)~Daca~\underline{b = 23}\implies 23+2c = 29\implies 2c= 6\implies \underline{c=3}$

$\boxed{\boxed{\bf Solutie~(a,b,c)\in\{(2,3,13);(2,7,11); (2,19,5);(2,23,3)\}}}$

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