Question

Ma ajutati va rog!!!!!​

Answer 1

Explicație pas cu pas:

$a < b \iff a + 9a < b + 9a \\ \iff 10a < 9a + b \implies a < \dfrac{9a + b}{10}$

$a < b \iff a + 8b < b + 8b \\ \iff 8b + a < 9b \implies \dfrac{8b + a}{9} < b$

$a < b \iff 71a < 71b \iff 71a + (10a + 9b) < 71b + (10a + 9b) \\81a + 9b < 80b + 10a \iff 9(9a + b) < 10(8b + a) \implies \dfrac{9a + b}{10} < \dfrac{8b + a}{9}$

atunci:

$a < \Big(\dfrac{9a + b}{10} ; \dfrac{8b + a}{9} \Big) < b \iff \Big(\dfrac{9a + b}{10} ; \dfrac{8b + a}{9} \Big) \subset \Big(a ; b \Big)$

q.e.d.