Question

If $△=\left|\begin{array}{ccc}-a& 2b& 0\\ 0& -a& 2b\\ 2b& 0& -a\end{array}\right|=0,$ then

• A. $\frac{1}{b}$ is a cube root of unity
• B. $a$ is one of the cube roots of unity
• C. $b$ is one of the cube root of $8$
• D. $\frac{a}{b}$ is a cube root of $8$

Answer 1

The correct option is D $\frac{a}{b}$ is a cube root of $8$

$△=\left|\begin{array}{ccc}-a& 2b& 0\\ 0& -a& 2b\\ 2b& 0& -a\end{array}\right|=0$

$\Rightarrow -a(a^2-0)-2b(0-4b^2)=0\Rightarrow 8b^3=a^3\Rightarrow \sqrt[3]{38}=\frac{a}{b}$