9. If \( x-\frac{1}{x}=\sqrt{6} \), then \( x^{2}+\frac{1}{x^{2}} \) is \( \begin{array}{ll}\text { (a) } 2 & \text { (b) } 4 \\ \text { (c) } 6 & \text { (d) } 8\end{array} \)

What is the greatest natural number \( x \), so that it leaves remainders 8 and 20 when 308 and 200 are divided by \( \times \) respectively.

VII. Find the solution(s) of the following system. \[ \left\{\begin{array}{r}x_{1}+x_{2}+x_{3}+x_{4}=0 \\ 2 x_{1}+2 x_{2}+3 x_{3}+4 x_{4}=0 \\ 2 x_{1}+2 x_{2}+2 x_{3}+2 x_{4}=0 \\ 3 x_{1}+3 x_{2}+4 x_{3}+5 x_{4}=0\end{array}\right. \]

\( \left\{\begin{array}{l}\text { Реши систему неравенств: } \\ (5 x+10)-5 \cdot(x+5)>5 x \\ (x-3)(x+8)<0\end{array}\right. \)

При каких значениях \( x \) верно, что \( 4 x+8<29 ? \)

48. If \( a=3-\sqrt{2} \) and \( b=\frac{a+1}{a-1} \) what is the value of \( b \)