6) \( (x-7)^{2}=(2-x)^{2} \)

20. \( \left(x^{2}-25\right) \sqrt{6-2 x}=0 \)

IV. Please calculate the following determinant \( \left|\begin{array}{llll}1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ 1 & 5 & 6 & 7 \\ 1 & 8 & 9 & 10\end{array}\right| \) (Write the answer for the questions on your answer sheet. 10 points)

20. \( \left(x^{2}-25\right) \sqrt{6-2 x}=0 \)

VI. Find the solution(s) of the following system. \[ \begin{array}{r}x+y+z=1 \\ 2 x+3 y+3 z=2 \\ x+2 y+2 z=1\end{array} \] (Write the answer for the questions on your answer sheet. 10 points)

9. \( \sqrt{x^{2}+x}=2-x \)