Question

find the term independent of x or absolute term in the expansion of
$| x^{2} + 1 \div x^{2} |^{9}$
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Answer 1

$\displaystyle \left(x^2 + \frac{1}{x^2}\right)^9\\\\\text{General term  =  } ^9 C_r (x^2)^{9-r} \left(\frac{1}{x^2}\right)^r\\\\= ^9C_r( x^{18-2r}) \left(\frac{1}{x^{2r}}\right)\\\\\text{For it to be independent of x: }\\\\2r = 18-2r \implies r = \frac{18}{4} = 4.5 \text{    which is not an integer }\\\\\text{Hence, there is no term which is independent of x.}$