Question

DAU COROANA!!
Calculează numerele prime a si b, stiind ca 13a+3b=104​

Answer 1

Răspuns:

$13 a + 3 b = 104$

$13a=104-3b$

$\frac{13a}{13}=\frac{104-3b}{13}$

$a=\frac{104-3b}{13}$

$a=-\frac{3b}{13}+8$

$13 a + 3 b = 104$

$3b=104-13a$

$\frac{3b}{3}=\frac{104-13a}{3}$

$b=\frac{104-13a}{3}$

Answer 2

$\it a,\ b\ -\ numere\ prime\\ \\ 13a+3b=104\ \ \ \ \ (1)\\ \\ 13a\ \d si\ 104\ sunt\ multiplii\ de \ 13\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 3b\in M_{13}\ \stackrel{b=prim}{\Longrightarrow}\ b=13\ \ \ \ \ (3)\\ \\ (1),\ (3) \Rightarrow 13a+39=104\Big|_{:13} \Rightarrow a+3=8\ \stackrel{a=prim}{\Longrightarrow }\ a=5$

Numerele cerute sunt: 5 și 13