Question

Ajutați mă pliz repede până la 23:00
DAU COROANĂ

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Answer 1

Explicație pas cu pas:

a)

$\dfrac{2 \sqrt{2} - 2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} } = \dfrac{(2 \sqrt{2} - 2 \sqrt{3})(\sqrt{3} + \sqrt{2}) }{ (\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) } =$

$= \dfrac{2 \sqrt{6} + 4 - 6 - 2 \sqrt{6} }{3 - 2}= \dfrac{ - 2}{1} = - 2 \in \mathbb{Q}$

b)

$a = \sqrt{3} + \sqrt{2} - \sqrt{3} = \sqrt{2}$

$b = - 2 + 2 + \sqrt{3} = \sqrt{3}$

$\dfrac{b}{a} = \dfrac{ \sqrt{3} }{ \sqrt{2} } = \dfrac{ \sqrt{6} }{2} = \sqrt{\dfrac{6}{4}}$

$\sqrt{\dfrac{6}{4}} = \sqrt{\dfrac{36}{24}} > \sqrt{\dfrac{36}{25}} = \dfrac{6}{5}$

$\sqrt{\dfrac{6}{4}} = \sqrt{\dfrac{24}{16}} < \sqrt{\dfrac{25}{16}} = \dfrac{5}{4}$

=>

$\dfrac{6}{5} < \dfrac{b}{a} < \dfrac{5}{4}$