Examine whether the following equation is quadratic or not: $x - \frac{1}{x} = 5$

$A$ 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: $2x^2 - 7x + 3 = 0$.

Obtain the roots of the following quadratic equation by using the quadratic formula: $9x^{2} + 7x - 2 = 0$.

The golden number $\frac{1+\sqrt{5}}{2}$ is one of the solutions of ...... .

Find two consecutive even positive integers,the sum of whose squares is $244$.