Solving the Equation and Finding the Required Expressions
Given the equation:
$a^{2} - 5a - 1 = 0$
and $a = 0$, we need to find the values of the following expressions:
(i) $a - \frac{1}{a}$
Since $a = 0$, we cannot find the value of this expression as it would result in a division by zero, which is undefined.
(ii) $a + \frac{1}{a}$
Again, since $a = 0$, we cannot find the value of this expression as it would result in a division by zero, which is undefined.
(iii) $a^{2} - \frac{1}{a^{2}}$
Since $a = 0$, we can substitute this value into the expression:
$a^{2} - \frac{1}{a^{2}} = 0^{2} - \frac{1}{0^{2}}$
Again, this expression is undefined due to the division by zero.
Therefore, we cannot find the values of the given expressions when $a = 0$ due to the presence of division by zero in each case.
