The set of real values of `a` for which the equation `(2a^(2)+x^(2))/(a^(3)-x^(3))-(2x)/(ax+a^(2)+x^(2))+(1)/(x-a)=0` has a unique solution is (a) (−∞,1) (b) (−1,∞) (c) (-1,1) (d) R−{0}

Options

A. `(-oo,1)`
B. `(-1,oo)`
C. `(-1,1)`
D. `R-{0}`

Answer

D

Explanation

`(d)` `(2a^(2)+x^(2))/(a^(3)-x^(3))-(2x)/(ax+a^(2)+x^(2))+(1)/(x-a) =0`
`implies (2x^(2)-3ax+a^(2))/(x^(3)-a^(3))=0 (x ne a)`
`implies 2x^(2)-3ax+a^(2)=0`
`implies x=a,(a)/(2)`
`:.(a)/(2)` is the only root if `(a)/(2) ne a`. ,brgt `:.a in (-oo,0)uu(0,oo)`.