The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

Let $\alpha, \beta$ be the roots of the equation $ax^2 + 2bx + c = 0$ and $\gamma, \delta$ be the roots of the equation $px^2 + 2qx + r = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then

Solve the given two equations and choose the correct option.
$I.$ $2x^2 - (4 + \sqrt{13})x + 2\sqrt{13} = 0$
$II.$ $10y^2 - (18 + 5\sqrt{13})y + 9\sqrt{13} = 0$

Solve the given two equations and select the correct option.

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is:

Solve the given two equations and select the correct answer from the given options.
$I. 2x^2 + 3x + 1 = 0$
$II. 12y^2 + 7y + 1 = 0$