Question

when a = 5+2 under root 6 find the value of number one under root a + 1 upon under root a

Answer 1

Hello,


We know that
$a = 5 + 2 \sqrt{6}$
Then 1/a will be equal to

After rationalizing...

$\frac{1}{a} = \frac{1}{5 + 2 \sqrt{6} } = 5 - 2 \sqrt{6}$


Now,

${( \sqrt{a} + \frac{1}{ \sqrt{a}} ) }^{2} = a + \frac{1}{a} + 2 \times \sqrt{a} \times \frac{1}{ \sqrt{a} } \\ \\ {( \sqrt{a} + \frac{1}{ \sqrt{a}} ) }^{2} = a + \frac{1}{a} +2 \\ \\ {( \sqrt{a} + \frac{1}{ \sqrt{a}} ) }^{2} =5 + 2 \sqrt{6} + 5 - 2 \sqrt{6} + 2 \\ \\ {( \sqrt{a} + \frac{1}{ \sqrt{a}} ) }^{2} =10 + 2 \\ \\ \sqrt{a} + \frac{1}{ \sqrt{a} } = \sqrt{12} = 2 \sqrt{3}$


Hope this will be helping you...