The uploaded image contains three mathematical exercises written in French. Here's a breakdown and explanation for each:

Exercice 1:

1. Comparer $x$ et $y$ dans les cas suivants :
   a) $x = 7 - 5\sqrt{2}$ et $y = \sqrt{99} - 7\sqrt{2}$
   b) $(x - y) = (2 - \sqrt{5})(1 - \sqrt{2})$

   2. Soient $a$ et $b$ deux nombres réels tels que :
   $-3 < a < 2$ et $b \in [5, 6]$.
   Encadrer :

   • $ab$
   • $b - 3a$
   • $2a^2 - b^2$

Exercice 2:

Soient $a$ et $b$ deux réels tels que : $2 < \sqrt{3a + 1} < 4$ et $|2b - 1| \leq 3$.

1. Montrer que :

   • $1 < a < 5$
   • $-1 < b < 2$

2. Donner un encadrement de :

   • $a - 2b$
   • $ab$

3. Soit $Y = (a - 2b) + cb - 3$. Montrer que $-11 < Y < 14$.

Exercice 3:

On considère les intervalles suivants :

• $A = ]-\infty, 0]$
• $B = ]a - 1, 8]$
• $C = [3, +\infty[$

1. Représenter sur la droite réelle les intervalles $A$, $B$, et $C$.
2. Déterminer :
   • $A \cap B$
   • $A \cap C$
   • $B \cup C$
   • $A \cup B$

Would you like a detailed step-by-step solution for each exercise? Let me know which one you'd like to start with!

Expanding your understanding

Here are five related questions to deepen your comprehension of this topic:

1. What methods can you use to compare two real numbers involving square roots?
2. How can you systematically find bounds for expressions involving two variables within given ranges?
3. How do you solve inequalities with absolute values like $|2b - 1| \leq 3$?
4. What are the properties of interval intersections and unions on the real line?
5. How does changing the endpoints of an interval affect its union or intersection with another interval?

Tip: When solving inequalities involving square roots or absolute values, it’s often helpful to rewrite the problem in terms of equivalent algebraic expressions!