$I. 3x^2 - 20x - 32 = 0$
$II. 2y^2 - 3y - 20 = 0$

Find the roots of the equation $\sqrt{3y+1} = \sqrt{y-1}$.

$Quantity \, 1$: Value of $y$. $A$ vessel contains $2.5 \, \text{liters}$ of water and $10 \, \text{liters}$ of milk. $20 \%$ of the contents of the vessel are removed. To the remaining contents,$x$ liters of water are added to reverse the ratio of water and milk. Then $y$ liters of milk are added again to reverse the ratio of water and milk. $Quantity \, 2$: $120 \, \text{liters}$.

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

Let $p, q \in Q$. If $2 - \sqrt{3}$ is a root of the quadratic equation $x^2 + px + q = 0$,then:

If the equations $x^{2}+2x-3=0$ and $x^{2}+3x-k=0$ have a common root,then the non-zero value of $k$ is: