Question

If
$a = \sqrt{3 + \sqrt{2 \:} }$
Then,

a + 1/a = ?​

Answer 1

Step-by-step explanation:

$a = \sqrt{3 + \sqrt{2} }$

$a + \frac{1}{a} = \sqrt{3 + \sqrt{2} } + \frac{1}{ \sqrt{3 + \sqrt{2} } }$

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

$= \frac{3 + \sqrt{2} + 1 }{ \sqrt{3 + \sqrt{2} } }$

$= \frac{4 + \sqrt{2} }{ \sqrt{3} + \sqrt[4]{2} }$