Solve the given two equations and select the correct option.
$I.$ $x = \sqrt[3]{2744}$
$II.$ $y = \sqrt{487}$

Number of integral values of $a$ for which both roots of the quadratic equation $x^2 - (2a + 3)x + a^2 + 3a = 0$ lie in the interval $(0, 4)$ is:

The solutions of the quadratic equation $(3|x| - 3)^2 = |x| + 7$ which belong to the domain of definition of the function $y = \sqrt{x(x - 3)}$ are given by

If $\frac{1}{\sqrt{\alpha}}$ and $\frac{1}{\sqrt{\beta}}$ are the roots of the equation $ax^2 + bx + 1 = 0$ $(a \neq 0, a, b \in R)$,then the equation $x(x + b^3) + (a^3 - 3abx) = 0$ has roots:

${x \in R : |x - 2| = x^2} = $

If $\frac{2x}{2x^2 + 5x + 2} > \frac{1}{x + 1}$,then