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The set of real values of a for which th...

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-1)=0` has a unique solution is

A

`(-oo,1)`

B

`(-1,oo)`

C

`(-1,1)`

D

`R-{0}`

Text Solution

Verified by Experts

The correct Answer is:
D
`(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)`.
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