If $a=b=c,$ then find the value of $\frac{(a+b+c)^{2}}{a^{2}+b^{2}+c^{2}}.$

Solve the given two equations and choose the correct answer from the given options.
$I.$ $x^{2} = 729$
$II.$ $y = \sqrt{729}$

If $x = \sqrt{7 + 4\sqrt{3}},$ then $x + \frac{1}{x} = $

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{12 \times 4}{x^{4/7}} - \frac{3 \times 4}{x^{4/7}} = x^{10/7}$
$II.$ $y^3 + 783 = 999$

The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} = 64$
$II.$ $2y^{2} + 25y + 72 = 0$