To determine the vitamins \( x \) and \( y \) that cause beri-beri and convulsions, respectively, we need to identify the specific vitamins associated with these conditions.
Step 1: Identify the Vitamin Deficiency for Beri-Beri
- Beri-Beri is caused by a deficiency of Vitamin B1 (Thiamine).
Step 2: Identify the Vitamin Deficiency for Convulsions
- Convulsions can be caused by a deficiency of Vitamin B6 (Pyridoxine).
Step 3: Match the Vitamins to the Options
- \( x \) (Beri-Beri) corresponds to Vitamin B1.
- \( y \) (Convulsions) corresponds to Vitamin B6. Final Answer: \[ \boxed{\text{B1, B6}} \] This corresponds to option (4).
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: