Question

If $x^g$+$\frac{1}{x^a}$ is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial?

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Answer 1

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

When a = 0 the expression becomes $x^0+\frac{1}{x^0}=x^0+x^{-0}$ = 1+1 = 2 $\because x^0=1$

So, it becomes a constant polynomial.