Question

Aflați numerele prime a, b, c, d dacă verifică egalitatea: 2a + 3b+4c + 48d = 174. Dau coroană!!!​

Answer 1

Explicație pas cu pas:

$2a + 3b + 4c + 48d = 174$

$3b = 174 - 2a - 4c - 48d \ \ \vdots \bf \ 2$

$\implies \bf b = 2$

$2a + 4c + 48d = 174 - 6$

$2a + 4c + 48d = 168\ \ \Big|:2$

$a + 2c + 24d = 84$

$a = 84 - 2c - 24d \ \ \vdots \bf \ 2$

$\implies \bf a = 2$

$2c + 24d = 84 - 2$

$2c + 24d = 82\ \ \Big|:2$

$c + 12d = 41 \iff c = 41 - 12d$

12d < 41 => d ∈ {2; 3}

d = 2 => c = 41 - 24 = 17

d = 3 => c = 41 - 36 = 5

numerele sunt:

$(a,b,c,d) \in \{(2;2;5;3);(2;2;17;2) \}$