Correct option: A.$2 + \frac{{3{x^2}}}{{4{a^2}}} + ....$
a
(a) ${\left( {\frac{{a + x}}{a}} \right)^{ - 1/2}} + {\left( {\frac{{a - x}}{a}} \right)^{ - 1/2}} = {\left( {1 + \frac{x}{a}} \right)^{ - 1/2}} + {\left( {1 - \frac{x}{a}} \right)^{ - 1/2}}$
$ = [ {1 + ( { - \frac{1}{2}} )\,\left( {\frac{x}{a}} \right) + \frac{{\left( { - \frac{1}{2}} \right)\,\left( { - \frac{3}{2}} \right)}}{{2.1}}{{\left( {\frac{x}{a}} \right)}^2} + ....} ]$
$ + \left[ {1 + \left( { - \frac{1}{2}} \right)\,\left( { - \frac{x}{a}} \right) + \frac{{\left( { - \frac{1}{2}} \right)\,\left( { - \frac{3}{2}} \right)}}{{2.1}}{{\left( { - \frac{x}{a}} \right)}^2} + ....} \right]$
$ = 2 + \frac{{3{x^2}}}{{4{a^2}}} + $.........
Here odd terms cancel each other.