Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{x} - \frac{(18)^{15/2}}{x^2} = 0$
$II.$ $\sqrt{y} = \frac{(19)^{9/2}}{y}$

Solve the given two equations and select the correct answer from the given options.
$I.$ $81x^2 - 9x - 2 = 0$
$II.$ $56y^2 - 13y - 3 = 0$

Solve the given two equations and select the correct option.
$I.$ $x^{2}-19x+84=0$
$II.$ $y^{2}-25y+156=0$

Let $p, q \in Q$. If $2 - \sqrt{3}$ is a root of the quadratic equation $x^2 + px + q = 0$,then:

If $\alpha, \beta$ are the roots of the equation $x^2 - px + q = 0$,then the quadratic equation whose roots are $(\alpha^2 - \beta^2)(\alpha^3 - \beta^3)$ and $\alpha^3\beta^2 + \alpha^2\beta^3$ is (where $S = p[p^4 - 5p^2q + 5q^2]$ and $P = p^2q^2(p^4 - 5p^2q + 4q^2)$).

Solve the given two equations and select the correct option.
$I.$ $7x - 3y = 13$
$II.$ $5x + 4y = 40$