Calculas-2-6-5-3-2-1-3-2-

Question Number 166496 by HongKing last updated on 21/Feb/22

Calculas :

\frac{2 \sqrt{6}}{\sqrt{5} + \sqrt{3} + \sqrt{2}} - \frac{1}{\sqrt{3} - \sqrt{2}} = ?

Commented by cortano1 last updated on 21/Feb/22

\frac{2 \sqrt{6}}{\sqrt{5} + (\sqrt{3} + \sqrt{2})} \times \frac{\sqrt{5} - (\sqrt{3} + \sqrt{2})}{\sqrt{5} - (\sqrt{3} + \sqrt{2})}

= \frac{2 \sqrt{6} (\sqrt{5} - \sqrt{3} - \sqrt{2})}{5 - (5 + 2 \sqrt{6})} = - \sqrt{5} + \sqrt{3} + \sqrt{2}

- ∙) - \sqrt{5} + \sqrt{3} + \sqrt{2} - (\frac{\sqrt{3} + \sqrt{2}}{3 - 2})

= - \sqrt{5} + \sqrt{3} + \sqrt{2} - \sqrt{3} - \sqrt{2} = - \sqrt{5}