On considère les nombres : \( a=3+\sqrt{5} \) et \( b=3-\sqrt{5} \) 1/ Montrer que : \( a=\sqrt{14+6 \sqrt{5}} \) et \( b=\sqrt{14-6 \sqrt{5}} \) 2/ Simplifier l'expression \( :(7+3 \sqrt{5})(3-\sqrt{5}) \sqrt{7-3 \sqrt{5}} \) 3/ Déduire la solution de l'équation : \( (7+3 \sqrt{5})(3-\sqrt{5}) \sqrt{7-3 \sqrt{5}}=\mathrm{t} \sqrt{2} \) avec \( t \in \mathbb{N} \) 4/ Montrer que : \( a^{3}=3^{3}(1+\sqrt{5})+5\left(3^{2}+\sqrt{5}\right) \) 5/ Montrer que : \( b^{3}=3^{3}(1-\sqrt{5})+5\left(3^{2}-\sqrt{5}\right) \) 6/ Soit \( x \in \mathbb{R}^{+} ; \)factoriser \( : x^{3}+2 \sqrt{2} \) et \( \quad x \sqrt{x}-1 \) 7/ Simplifier le nombre : \( \frac{x \sqrt{x}+y \sqrt{y}}{\sqrt{x}+\sqrt{y}} \) 8/ Soit \( a \) un entier naturel non nul, on pose : \( \boldsymbol{A}=\boldsymbol{a}+\frac{1}{a} \) Calculer en fonction de A les expressions suivantes : \( a^{2}+\frac{1}{a^{2}} \quad ; \quad a^{3}+\frac{1}{a^{3}} \)

5. \( \left(16 x^{2}\right)^{-1} \)

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. \( x=-30 \)

В ар иант 2 1. Преобразуйте в многочлен. а) \( (x-6)^{2} ; \)

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 \( \beta \).

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