Question

If a² - 3a - 1 = 0 and a ≠ 0, find : `"a"  + (1)/"a"`

Answer 1

`"a"  - (1)/"a"` = 3

Squaring both sides, we get

`("a" - 1/"a")^2`

= `"a"^2 + (1)/"a"^2 - 2`

= 9

⇒ `"a"^2 + (1)/"a"^2`

= 11.

Now,
`("a" + 1/"a")^2`

= `"a"^2 + (1)/"a"^2`

= 11 + 2
= 13

⇒ `"a" + (1)/"a"^2`

= ±`sqrt(13)`.