Question

Calcule a razão da PG

 

$<var>(3/\sqrt{5}-2;\ \ 6/5-2\sqrt{5};\ \ 12/5\sqrt{5}-10 ...)</var>$

Answer 1

$<var>\frac{6}{5-2\sqrt{5}} \cdot \frac{\sqrt{5}-2}{3} = \frac{2\sqrt{5}-4}{5-2\sqrt{5}} \\ \frac{2\sqrt{5}-4}{5-2\sqrt{5}} \cdot \frac{5+2\sqrt{5}}{5+2\sqrt{5}} = \\ \frac{10\sqrt{5}-8\sqrt{5}}{25-4\cdot 5} = \frac{2\sqrt{5}}{5} </var>$