If $x^{a} + \frac{1}{x^{b}}$ is a polynomial and if it is given that a = b, then the value of $a$ is .

0.0

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-1

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Solution

The correct option is A 0.0
$x^{a} + \frac{1}{x^{b}} = x^{a} + x^{- b}$
Since a = b,
$x^{a} + \frac{1}{x^{b}} = x^{a} + x^{- a}$
For the expression $x^{a} + x^{- a}$ to be a polynomial, a and -a must be whole numbers.
Thus, a = 0 is the only possibility.

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