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

Solve the given two equations and select the correct answer from the given options.
$I.$ $63x - 194\sqrt{x} + 143 = 0$
$II.$ $99y - 255\sqrt{y} + 150 = 0$

If one root of the quadratic equation $ax^2 + bx + c = 0$ is equal to the $n^{th}$ power of the other root,then the value of $(ac^n)^{\frac{1}{n+1}} + (a^nc)^{\frac{1}{n+1}} = $

Find the complete set of values of $k$ for which the equation $4^x - (k + 2)2^x + 2k = 0$ has exactly one positive root.

If the ratio of the roots of $x^2 + bx + c = 0$ and $x^2 + qx + r = 0$ is the same,then:

Sum of the solutions of the equation $[x^2] - 2x + 1 = 0$ is (where $[.]$ denotes the greatest integer function).