The roots of the equation $a(x^2 + 1) - (a^2 + 1)x = 0$ are

Solve the given two equations and select the correct answer from the given options.
$I. 63x - 94\sqrt{x} + 35 = 0$
$II. 32y - 52\sqrt{y} + 21 = 0$

If $x$ is a solution of the equation $\sqrt{2x + 1} - \sqrt{2x - 1} = 1$ where $x \ge \frac{1}{2}$,then $\sqrt{4x^2 - 1}$ is equal to:

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

If $\alpha, \beta, \gamma$ are roots of $x^3 - 2x^2 + 3x - 2 = 0$,then the value of $\left( \frac{\alpha\beta}{\alpha + \beta} + \frac{\alpha\gamma}{\alpha + \gamma} + \frac{\beta\gamma}{\beta + \gamma} \right)$ is

If the sum of the roots of the equation $\lambda x^2 + 2x + 3\lambda = 0$ is equal to their product,then $\lambda = $