Question

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Answer 1

Explicație pas cu pas:

$\bigg( \sqrt{ \dfrac{ \sqrt{5} - \sqrt{2} }{\sqrt{5} + \sqrt{2}} } - \sqrt{ \dfrac{ \sqrt{5} + \sqrt{2} }{\sqrt{5} - \sqrt{2}} } \bigg) \cdot \Big( \dfrac{1}{3} \Big)^{-1} =$

$= \bigg( \sqrt{ \dfrac{ {(\sqrt{5} - \sqrt{2})}^{2} }{(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})} } - \sqrt{ \dfrac{ {( \sqrt{5} + \sqrt{2})}^{2} }{(\sqrt{5} - \sqrt{2})(\sqrt{5} + \sqrt{2})} } \bigg) \cdot \Big( {3}^{ - 1} \Big)^{-1}$

$= \bigg( \dfrac{ | \sqrt{5} - \sqrt{2} | }{ \sqrt{5 - 2} } - \dfrac{ | \sqrt{5} + \sqrt{2} | }{ \sqrt{5 - 2} } \bigg) \cdot 3$

$= \dfrac{ \sqrt{5} - \sqrt{2} - ( \sqrt{5} + \sqrt{2})}{ \sqrt{3} } \cdot 3$

$= \dfrac{ (\sqrt{5} - \sqrt{2} - \sqrt{5} - \sqrt{2}) \cdot \sqrt{3} }{3} \cdot 3$

$= - 2 \sqrt{2} \cdot \sqrt{3} = \bf - 2 \sqrt{6}$