4. \( \begin{array}{l}\text { Является ли решением уравнения } 10 x+y=12 \text { пара чисел } \\ (3 ;-20),(-2 ; 12),(0,1 ; 11),(1 ; 2),(2 ; 1) ?\end{array} \)

b) Montrer que si \( x<y \) alors \( \sqrt{x+y+2 \sqrt{x y}+\sqrt{x+y-2 \sqrt{x y}}=2 \sqrt{y}} \) c) Montrer que si \( x \geq 2 \) alors \( (\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}})^{2}=4(x-1) \) Bonus Démontrer que \( \sqrt{2} \) est irrationnelle

Question (2): Solve all the following Problem Marks] a) If \( A=\left[\begin{array}{cc}0 & -1 \\ 2 & 5 \\ 1 & 3\end{array}\right] \) and \( B=\left[\begin{array}{cc}-1 & 0 \\ 5 & -1 \\ 3 & 2\end{array}\right] \), find \( 3 A-B \). b) If \( A=\left[\begin{array}{cc}1 & 2 \\ -1 & 0 \\ 0 & 3\end{array}\right] \), and \( B=\left[\begin{array}{ccc}0 & -1 & 2 \\ -4 & 1 & 0\end{array}\right] \), find \( B A \). c) Find the inverse of the Matrix \( A=\left[\begin{array}{ccc}4 & -2 & 1 \\ 5 & 0 & 3 \\ -1 & 2 & 6\end{array}\right] \) d) Solve the following system of equations using jacobi method. \( x+y+z=9 \) \( \quad 2 x+5 y+7 z=52 \) \( 2 x+y-z=0 \)

2) Calculer puis écrire sans radical au dénominateur les expressions suivantes : \( C=\frac{\sqrt{3}}{\sqrt{3}+1}-\frac{\sqrt{3}-1}{\sqrt{3}+2}- \) et \( D=\left(\sqrt{5}+\frac{1}{\sqrt{5}}\right)^{2} \) 3) Soient \( x, y \) et \( z \) trois nombres réels strictement positifs. a) Montre que si \( x y+y z+x z=0 \) alors \( \frac{y+z}{x}+\frac{x+z}{y}+\frac{x+y}{z}=-3 \). b) Montrer que si \( x<y \) alors \( \sqrt{x+y+2 \sqrt{x y}}+\sqrt{x+y-2 \sqrt{x y}}=2 \sqrt{y} \) c) Montrer que si \( x \geq 2 \) alors \( (\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}})^{2}=4(x-1) \)

if: \( x=\frac{5}{4} y \), what is \( \sqrt{x^{2}-y^{2}} \) \( \begin{array}{llll}\text { 1) } 1 & \text { 2)2 } & \text { 3) } 3 & 4) 4\end{array} \)

Ungkapkan fungsi kuadratik, \( f(x)=2 x^{2}+8 x+11 \) sebagai \( f(x)=a(x-h)^{2}+k \) di mana \( a, h \) dan \( k \) ialah pemalar. Kemudian lakarkan graf fungsi kuadratik tersebut. Sekiranya nilai a yang diperoleh menjadi lebih besar, nyatakan kesan perubahan tersebut terhadap bentuk dan kedudukan graf. Express the quadratic function, \( f(x)=2 x^{2}+8 x+11 \) as \( f(x)=a(x-h)^{2}+k \) where \( a, h \) and \( k \) are constants. Then sketch the graph of the quadratic function. If the obtained value of a becomes greater, state the effect of the change on the shape and position of the graph.