Question

 If a = 2√2 - √7 then a + 1/a is *​

Answer 1

$a = 2 \sqrt{2} - \sqrt{7}$

$\frac{1}{a} = \frac{1}{2 \sqrt{2} - \sqrt{7} }$

$= \frac{2 \sqrt{2} + \sqrt{7} }{2 \sqrt{2} - \sqrt{7} \times (2 \sqrt{2} + \sqrt{7} ) }$

$= \frac{2 \sqrt{2} + \sqrt{7} }{8 - 1}$

$= 2 \sqrt{2} + \sqrt{7}$

add those

$2 \sqrt{2} - \sqrt{7} + 2 \sqrt{2} + \sqrt{7}$

$= 4 \sqrt{2}$