Question

$(\frac{a}{a+x}{)}^{\frac{1}{2}}$ + $(\frac{a}{a-x}{)}^{\frac{1}{2}}$ =

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$(\frac{a+x}{a}{)}^{\frac{-1}{2}}$ + $(\frac{a-x}{a}{)}^{\frac{-1}{2}}$ =$(1+\frac{x}{a}{)}^{\frac{-1}{2}}+(1-\frac{x}{a}{)}^{\frac{-1}{2}}$

=[1 + (- $\frac{1}{2}$)( $\frac{x}{a}$) + $\frac{(-\frac{1}{2})(-\frac{3}{2})}{2.1}$$(\frac{x}{a}{)}^2$ + ........]

+ $[1+(-\frac{1}{2}\left)\right(-\frac{x}{a})+\frac{(-\frac{1}{2})\left(\frac{3}{2}\right)}{2.1}(-\frac{x}{a}{)}^2+........]$

= 2 + $\frac{3x^2}{4a^2}$ + ......

Here odd terms cancel each other.