Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} = 49$
$II.$ $y^{2} + 15y + 56 = 0$

Let $x_1, x_2, x_3 \in R - \{0\}$,$x_1 + x_2 + x_3 \neq 0$ and $\frac{1}{x_1} + \frac{1}{x_2} + \frac{1}{x_3} = \frac{1}{x_1 + x_2 + x_3}$. Then $\frac{1}{x_1^n + x_2^n + x_3^n} = \frac{1}{x_1^n} + \frac{1}{x_2^n} + \frac{1}{x_3^n}$ holds good for:

Let $f(x) = x^2 - x + k - 2$,$k \in R$. Then the complete set of values of $k$ for which $y = |f(|x|)|$ is non-derivable at $5$ distinct points is:

If $c > 0$ and the equation $3ax^2 + 4bx + c = 0$ has no real root,then :-

Consider the equation $x^2 + \alpha x + \beta = 0$ having roots $\alpha, \beta$ such that $\alpha \neq \beta$. Also consider the inequality $| |y - \beta| - \alpha | < \alpha$,then:

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt{2304}$
$II.$ $y^2 = 2304$