Question

The value of $\left|\begin{array}{ccc}-1& 2& 1\\ 3+2\sqrt{2}& 2+2\sqrt{2}& 1\\ 3-2\sqrt{2}& 2-2\sqrt{2}& 1\end{array}\right|$ is equal to

• A. zero
• B. $-16\sqrt{2}$
• C. $-8\sqrt{2}$
• D. one of these

Answer 1

Answer: (B)

$-16\sqrt{2}$

$\left|\begin{array}{ccc}-1& 2& 1\\ 3+2\sqrt{2}& 2+2\sqrt{2}& 1\\ 3-2\sqrt{2}& 2-2\sqrt{2}& 1\end{array}\right|$

$-1(2+2\sqrt{2}-2+2\sqrt{2})-2(3+2\sqrt{2}-3+2\sqrt{2})+1\left[\right(3+2\sqrt{2}\left)\right(2-2\sqrt{2})-(2+2\sqrt{2}\left)\right(3-2\sqrt{2}\left)\right]$

$=-1\left(4\sqrt{2}\right)-2\left(4\sqrt{2}\right)+1(-4\sqrt{2})=-16\sqrt{2}$