Question

Determinati numerele prime , a,b,c daca : 2a+6b+7c=66                                    dau coroana      URGENT 

Answer 1

   
[tex]a,\;b,\;c~~~sunt~numere ~prime \\ 2a+6b+7c=66 \\ 2a = numar ~par \\ 6b = numar ~par \\ 66 = numar~par \\ \Rightarrow~~7c ~trebuie ~sa ~fie~ par. \\ \text{Singurul numar prim par este 2. } [/tex]

[tex]\Rightarrow~~c=\boxed{2} \\ 2a+6b+7\times 2=66 \\ 2a+6b=66-14 \\ 2a+6b = 52 ~~~~~|:2 \\ a+3b=26 \\ a=26-3b ~~~~~(Dam~valori~lui~b) \\ b=\boxed {1}~~\Longrightarrow~~a=26-3\times 1 = 26-3 = \boxed{23} \\ b=\boxed {3}~~\Longrightarrow~~a=26-3\times 3 = 26-9 = \boxed{17} \\ b=\boxed {5}~~\Longrightarrow~~a=26-3\times 5 = 26-15 = \boxed{11} \\ b=\boxed {7}~~\Longrightarrow~~a=26-3\times 7 = 26-21 = \boxed{5} [/tex]

[tex]Avem \; solutiile: \\ S1: ~~~\boxed{a=23,~b=1,~c=2} \\ S2: ~~~\boxed{a=17,~b=3,~c=2} \\ S3: ~~~\boxed{a=11,~b=5,~c=2} \\ S4: ~~~\boxed{a=5,~b=7,~c=2} \\ [/tex]