Hi Bober. Some hints on the problems you've been asking about:

3.24: If we make the substitution $u = \sqrt{x}$, this becomes a quadratic in the variable $u$. Then think about how $u$ and $x$ are related to make sure a real solution exists. In the cases where it make sense, what is $x$ (in terms of $k$).

3.26: If $r$ and $s$ are the integer roots, how are they related to $a$ and $b$? One of the example problems from class should be similar.

3.29: First think about what happens when $m$ is a specific value, like $m = 1$ or $m = 2$. How would you solve the system of equations for $(x,y)$? Is there a step here where you solve a quadratic equation?

3.30: What happens when you expand $(1+x_1)(1+x_2)$? Then try using Vieta's formulas.