If $x^{a}$ + $\frac{1}{x^{b}}$ is a polynomial in one variable and if it is given that $a = b$ , then this is a polynomial for $a =$ ___

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Solution

Given, $x^{a}$ + $\frac{1}{x^{b}} = x^{a} + x^{- b}$
Since, $a = b$
$\Rightarrow x^{a} + \frac{1}{x^{b}} = x^{a} + x^{- a}$
For the expression, $x^{a} + x^{- a}$ to be a polynomial, $a$ and $- a$ must be whole numbers.
Thus, $a = 0$

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