Rút gọn biểu thức

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VD2: N.
$\frac{4 + \sqrt{3}}{4 - \sqrt{3}}$ = $\frac{\sqrt{27}-10\sqrt{2}}{\sqrt{4+\sqrt{3}}}$

70°: $\gamma = \sqrt{2} \left( \sqrt{4+\sqrt{3}} - \sqrt{4-\sqrt{3}} \right)$

= $8 + 2\sqrt{13}$

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

= $\sqrt{(4+\sqrt{3}) + 2\sqrt{4+\sqrt{3}}\cdot\sqrt{4-\sqrt{3}} + (4+\sqrt{3})}$

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

= $\sqrt{2 \left( \sqrt{4+\sqrt{3}} + \sqrt{4-\sqrt{3}} \right)} + \sqrt{15 - \sqrt{2}}^2$

= $\sqrt{4+\sqrt{3}} + \sqrt{4-\sqrt{3}}$

= $\sqrt{2 + 5 - \sqrt{2}} = 5$