Question

If a + `1/a` = m and a ≠ 0; find in terms of 'm'; the value of `a^2 - 1/a^2`.

Answer 1

`a^2 - 1/a^2 = ( a + 1/a )(a - 1/a )`         ...[Since a² - b² = (a + b)(a - b)]

= `m(+- sqrt(m^2 - 4) )`

= `+-msqrt(m^2 - 4)`