The sum of the reciprocals of Rehman's ages,(in $years$) $3$ years ago and $5$ years from now is $\frac{1}{3}$. Find his present age. (in $years$)

Check whether the following is a quadratic equation:
$x^{3}-4x^{2}-x+1=(x-2)^{3}$

Check whether the following is a quadratic equation:
$(x-3)(2x+1) = x(x+5)$

$A$ pole has to be erected at a point on the boundary of a circular park of diameter $13 \, m$ in such a way that the differences of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7 \, m$. Is it possible to do so? If yes,at what distances from the two gates should the pole be erected?

Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $2x^{2} + x - 4 = 0$.

Check whether the following is a quadratic equation:
$x(x+1)+8=(x+2)(x-2)$