Question

Сократите дроби

1.6√2-9/(1-√2)²
2.4√6-14/(1-√6)²​

Answer 1

Решение:

$\frac{6\sqrt{2}-9 }{(1-\sqrt{2} )^2} = \frac{3(2\sqrt{2} - 3)}{1-2\sqrt{2}+2} =\frac{3(2\sqrt{2} - 3)}{3-2\sqrt{2}} = -\frac{3(2\sqrt{2} - 3)}{2\sqrt{2}-3} = -3$

$\frac{4\sqrt{6}-14}{(1-\sqrt{6})^2} = \frac{2(2\sqrt{6} - 7)}{1-2\sqrt{6}+6} =\frac{2(2\sqrt{6} - 7)}{7-2\sqrt{6}} = -\frac{2(2\sqrt{6} - 7)}{2\sqrt{6}-7} = -2$