If the roots of the equation $5x^2 - 7x + k = 0$ are reciprocals of each other,then the value of $k$ is:

If the sum of the roots of the equation ${x^2} + px + q = 0$ is equal to the sum of their squares,then

If $|{x^2} - x - 6| = x + 2$,then the values of $x$ are

Solve the given two equations and select the correct answer from the given options.
$I. 63x - 94\sqrt{x} + 35 = 0$
$II. 32y - 52\sqrt{y} + 21 = 0$

Divide $16$ into $2$ parts such that twice the square of the larger part exceeds the square of the smaller part by $164$.

If $\alpha$ and $\beta$ are roots of the equation $x^2 - 4\sqrt{2}kx + 2e^{4\ln k} - 1 = 0$ for some $k$, and $\alpha^2 + \beta^2 = 66$, then $\alpha^3 + \beta^3$ is equal to: (in $\sqrt{2}$)