
The reaction shown in the question is a Wurtz-Fittig reaction. This reaction involves the reaction of an alkyl halide (R-X) with sodium in dry ether, leading to the formation of an alkane (X) or an alkylated product (Y). It is a combination of the Wurtz reaction (for alkyl halide formation) and the Fittig reaction (for aryl halide formation).
The Wurtz-Fittig reaction is a combination of both reactions and is used to form aryl and alkyl products.
If the roots of $\sqrt{\frac{1 - y}{y}} + \sqrt{\frac{y}{1 - y}} = \frac{5}{2}$ are $\alpha$ and $\beta$ ($\beta > \alpha$) and the equation $(\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0$ has real roots, then a possible value of $y$ is: