Question

if A=5+2√6 then find √A+1/√A​

Answer 1

$\huge{\bold{SOLUTION:-}}$

$\sqrt{A} = \sqrt{5 + 2 \sqrt{6} }$

$\sqrt{(3 + 2) + 2 \sqrt{3 \times 2} }$

$\sqrt{ \sqrt{ {3}^{2} } + \sqrt{ {2}^{2} } + 2 \sqrt{3} \sqrt{2} }$

$\sqrt{ ({ \sqrt{3} + \sqrt{2} })^{2} }$

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

Now the value of

$\sqrt{A} + \frac{1}{ \sqrt{A} }$

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

$\sqrt{3} + \sqrt{2} + \frac{ \sqrt{3} - \sqrt{2} }{3 - 2}$

$2 \sqrt{3} \: \: is \: the \: answer$