1) a) Comparer \( 5 \sqrt{3} \) et \( 6 \sqrt{2} \) b) Déduire la comparaison de \( \frac{1}{5 \sqrt{3}-2} \) et \( \frac{1}{6 \sqrt{2}-2} \) 2) \( x \) et \( y \) deux nombres réels tel que : \( \sqrt{3} \leq \sqrt{2 x-1} \leq \sqrt{5} \) et \( -\frac{13}{2} \leq \frac{2 y-3}{2} \leq-\frac{7}{2} \) a) Montrer que \( 2 \leq x \leq 3 \) et \( -5 \leq y \leq-2 \) b) Encadrer : \( \quad 2 x-y \quad \);; \( x y \quad ; ; x^{2}+y^{2}+3 \) c) Sachant que \( 4 x+y=8 \), Calculer \( H=\sqrt{(8 x-4)^{2}}-\sqrt{(2 y+4)^{2}}+3 \)

Encuentra el resultado utilizando la propiedad de potencias: \( (a^{2b})^{3} \)

Enter the correct answer in the box. Rewrite the expression \( 2 \sqrt[4]{x^{7}} \) using rational exponents. \( \begin{array}{lll}\frac{\square}{\square} & \text { (ㅁ) } \mid \text { 미 } \square^{\square} \mid+--\end{array} \)

What is the solution to the equation? \( \sqrt[3]{2 x+5}=5 \) A. 240 B. 65 ( \( ) 60 \) D. 6 D. 5

Find the value of \( m \) if \( \alpha+\beta=-2 \). (b) Seterusnya, bentukkan persamaan kuadratik dengan punca-punca \( \alpha \) dan \( \beta \). Hence, form a quadratic equation with roots \( \alpha \) and \( \beta \).

It would take Charlene and Gina 18 minutes to organize Charlene's comic book collection if they work together. If Gina works alone, it would take her 15 minutes longer than it would take Charlene working alone. When \( x \) represents the number of minutes it takes Charlene to organize the comic book collection working alone, the situation is represented by this equation: \( \frac{1}{x}+\frac{1}{x+15}=\frac{1}{18} \), Which value is a solution of the rational equation that must be discarded because of the context? A. \( x=0 \) B. \( x=-9 \) C. \( x=-15 \) D. \( x=-30 \)