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Find the coefficient of x^2in(a/(a+x))^(...

Find the coefficient of `x^2in(a/(a+x))^(1//2)+(a/(a-x))^(1//2)`

Text Solution

Verified by Experts

The correct Answer is:
`3/4 a^(2)`
`((a+x)/(a))^(-1//2)+((a-x)/(a))^(-1//2)=(1-(x)/(a))^(-1//2)+(1-(x)/(a))^(-1//2)`
`=[1+(-1/2)(x/a)+((-(1)/(2))(-3/2))/(2.1)(x/a)^(2)+"......"]+[1+(-1/2)(-x/a)+((-1/2)(-3/2))/(2.1)(-x/a)^(2)+"....."]`
`= 2+(3x^(2))/(4a^(2))`
Hence, the coefficeint of `x^(2)` is `(3//4)a^(2)`.
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