The equation of the normal to the curve ay² = x³ at the point (am², am³) is

If A is a square matrix of order 3 and |A| = $$-$$ 5, then |adj A| is

The simplest form of $${\tan ^{ - 1}}\left[ {{{\sqrt {1 + x} - \sqrt {1 - x} } \over {\sqrt {1 + x} + \sqrt {1 - x} }}} \right]$$ is

If for the matrix $$A = \left[ {\matrix{ \alpha & { - 2} \cr { - 2} & \alpha \cr } } \right]$$, | A³ | = 125, then the value of $$\alpha$$ is