Question

Dacă a<b,arătați că
$a < \frac{2a + 5b}{7} < b$
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Answer 1

$a&lt;b\Big|\cdot 2 \Rightarrow 2a&lt;2b\Big|+5b \Rightarrow 2a+5b &lt; 7b\quad (*) \\\\ a&lt;b\Big|\cdot 5 \Rightarrow 5a&lt;5b\Big|+2a \Rightarrow 7a&lt;2a+5b\quad (**) \\ \\ \\ \text{Din }(*)\text{ si }(**) \Rightarrow 7a&lt;2a+5b&lt;7b\Big|:7 \Rightarrow \\ \\ \Rightarrow a &lt; \dfrac{2a+5b}{7}&lt;b$