Solve the given two equations and select the correct answer from the given options.
$I.$ $(x+y)^{2} = 3136$
$II.$ $y+2513 = 2569$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-7 \sqrt{7} x+84=0$
$II.$ $y^{2}-5 \sqrt{5} y+30=0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $7x^2 + 16x - 15 = 0$
$II.$ $y^2 - 6y - 7 = 0$

If $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 - 100x^3 + 2x^2 + 4x + 10 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\delta}$ is equal to:

Sum of all distinct integral values of $\alpha$ such that the equation $x^2 - \alpha x + \alpha + 1 = 0$ has integral roots,is equal to-

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 - x - 1 = 0$,then the equation whose roots are $\frac{1}{\beta + \gamma}, \frac{1}{\gamma + \alpha}, \frac{1}{\alpha + \beta}$ is: