Question

12
17 V5
$\frac{2 + 3 \sqrt{ \times \\ } }{?}$
$\frac{2 + 3 \sqrt{ \times } }{ \sqrt{3 + \sqrt{5} } } =$
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Answer 1

Respuesta:

$=\frac{\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}\left(2+3\sqrt{X}\right)}{4}$

Explicación paso a paso:

$\frac{2+3\sqrt{X}}{\sqrt{3+\sqrt{5}}}\\\\=\frac{\left(2+3\sqrt{X}\right)\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}\sqrt{3+\sqrt{5}}}\\\\=\frac{\sqrt{3+\sqrt{5}}\left(2+3\sqrt{X}\right)}{3+\sqrt{5}}\\\\=\frac{\sqrt{3+\sqrt{5}}\left(2+3\sqrt{X}\right)\left(3-\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}\\\\=\frac{\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}\left(2+3\sqrt{X}\right)}{4}$