The image contains mathematical problems primarily focusing on solving systems of equations, quadratic functions, and other algebraic inequalities and conditions. Here’s a brief overview of the visible tasks:

Key Problems to Address:

1. Problem 17 - Solve the systems of equations in $\mathbb{R}^2$.

   • Part (a): $x + xy + y = 5$ and $x^2 + y^2 = 5$.
   • Part (b): $\frac{x}{y} = \frac{5}{2}$ and $x^2y + xy^2 = 6$.
   • Part (c): $\frac{1}{x} + \frac{1}{y} = 3$ and $x^2 + y^2 = \frac{3}{4}$.

2. Problem 18 - Find values of $c$ such that the given system has unique solutions.

3. Problem 19 - Consider the equation $mx^2 - 2x - m - 1 = 0$ for real values $m$.

   • Part (a) requests proof that the roots are distinct and real for any $m$.
   • Parts (b) and (c) explore finding values of $m$ with specific conditions on roots.

4. Problem 22 - Determine natural numbers $n$ that make an equation valid.

5. Problem 27 - Find a quadratic function given specific points on its graph.

Would you like me to solve any specific problem or provide detailed solutions for one of these sections?