Solve the given two equations and select the correct answer from the given options.
$I. \quad x - 7\sqrt{x} + 12 = 0$
$II. \quad y - 5\sqrt{y} + 6 = 0$

If $\left(\frac{p^{-1} q^{2}}{p^{3} q^{-2}}\right)^{\frac{1}{3}}+\left(\frac{p^{5} q^{-3}}{p^{-2} q^{3}}\right)^{\frac{1}{3}}=p^{a} q^{b},$ then the value of $a+b,$ where $p$ and $q$ are different positive positive primes,is

If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$,where $p \neq q$,then $pq$ is equal to

If the roots of the equation $x^2 - 5x + 16 = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2 + \beta^2$ and $\frac{\alpha \beta}{2}$,then:

If $\alpha, \beta$ are the roots of ${x^2} + px + q = 0$ and $\alpha + h, \beta + h$ are the roots of ${x^2} + rx + s = 0$,then

Solve the given two equations and select the correct answer from the given options.
$I. 2x^2 + 3x + 1 = 0$
$II. 12y^2 + 7y + 1 = 0$