Question

4. Determinați numerele naturale nenule a, b, c, pentru care:​

Answer 1

Răspuns:

a = 10; b = 12; c = 18

Explicație pas cu pas:

$14a + 14b = 11a + 11c \\ = > 3a + 14b = 11c$

$15a + 15c = 14b + 14c \\ = > 15a + c = 14b$

$15a + 15b = 11b + 11c \\ = > 15a + 4b = 11c$

$din \: (1) \: si \: (2) = > 18a + c = 11c \\ = > c = \frac{9a}{5}$

$din \: (1) \: si \: (3) = >3a + 14b = 15a + 4b \\ = > b = \frac{6a}{5}$

$\frac{ 2a \times \frac{6a}{5} - a \times \frac{9a}{5} }{a +3 \times \frac{6a}{5} - \frac{9a}{5}} \\ = \frac{ \frac{12 {a}^{2} }{5} - \frac{9 {a}^{2} }{5} }{ \frac{5a + 18a - 9a}{5} } = \frac{3 {a}^{2} }{14a} = \frac{3a}{14} \\ = > \frac{3a}{14} = \frac{15}{7} \\ = > a = 10 \\ = > b = 12 \\ = > c = 18$