The image you uploaded contains a mathematical assignment focused on finding the values of expressions involving square roots and fractions.

Here’s a breakdown of the key parts of the assignment shown in the image:

1. First Problem:

   • The task is to find the values of $\alpha^2$ and $\beta^2$.
   • $\alpha$ and $\beta$ are defined as: $\alpha = \sqrt{5 + 2\sqrt{13}} - \sqrt{5 - 2\sqrt{13}}$ $\beta = \sqrt{5 + 2\sqrt{13}} + \sqrt{5 - 2\sqrt{13}}$
   • The solution involves squaring both expressions for $\alpha$ and $\beta$ to find $\alpha^2$ and $\beta^2$ respectively.

2. Second Problem:

   • You are given the task to prove that: $\sqrt{12 + 7\sqrt{5}} = \sqrt{a} + \sqrt{b}$
   • Here, $a$ and $b$ are positive integers.
   • You need to equate and solve to find the values of $a$ and $b$.

Would you like me to go through the steps to solve these problems in detail, or is there a particular part you'd like me to focus on?