If a=7—4√3, find √a+1/√a

{tex}\eqalign{ & Here,a = 7 - 4\sqrt 3 \left( {Given} \right) \cr & Let{\text{ }}x = \sqrt a + \frac{1}{{\sqrt a }} \cr & \Rightarrow {x^2} = {\left( {\sqrt a + \frac{1}{{\sqrt a }}} \right)^2} \cr & \Rightarrow {x^2} = {\left( {\sqrt a } \right)^2} + {\left( {\frac{1}{{\sqrt a }}} \right)^2} + 2 \times \sqrt a \times \frac{1}{{\sqrt a }} \cr & \Rightarrow {x^2} = a + \frac{1}{a} + 2 \cr & \Rightarrow {x^2} = 7 - 4\sqrt 3 + \frac{1}{{7 - 4\sqrt 3 }} + 2 \cr & \Rightarrow {x^2} = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 + 2\left[ {\because \frac{1}{{7 - 4\sqrt 3 }} \times \frac{{7 + 4\sqrt 3 }}{{7 + 4\sqrt 3 }} = 7 + 4\sqrt 3 } \right] \cr & \Rightarrow {x^2} = 16 \cr & \Rightarrow x = \pm 4 \cr & \Rightarrow \sqrt a + \frac{1}{{\sqrt a }} = \pm 4 \cr} {/tex}