(i)
$\begin{array}{l}
x^{2}-\frac{2}{x}=x^{2} \\
\Rightarrow x^{2}+2=x^{3} \\
\Rightarrow x^{3}-x^{2}-2=0
\end{array}$

$\left(x^{3}-x^{2}-2\right)$ is not a quadratic polynomial.

$\therefore x^{3}-x^{2}-2=0$ is not a quadratic equation.

(ii) $x^{2}-\frac{1}{x^{2}}=5$ $\Rightarrow x^{4}-1=5 x^{2}$
$\Rightarrow x^{4}-5 x^{2}-1=0$

$\left(x^{4}-5 x^{2}-1\right)$ is a polynomial with degree 4

$\therefore x^{4}-5 x^{2}-1=0$ is not a quadratic equation.