Question

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

Answer 1

Given that a + `1/a` = m
Now consider the expansion of `( a + 1/a )^2` :
`( a + 1/a )^2 = a^2 + 1/a^2 + 2`

⇒ m² = a² + `1/a^2` + 2
⇒ a² + `1/a^2` = m² - 2
Now consider the expansion of `( a - 1/a )^2` :
`( a - 1/a )^2 = a^2 + 1/a^2 - 2`

⇒ `( a - 1/a )^2 = m^2 - 2 - 2`

⇒ `( a - 1/a )^2 = m^2 - 4`

⇒ `( a - 1/a ) = +-sqrt(m^2 - 4)`