# Expansions-7

### From Homeworkwiki

**If a ^{ 2 } - 5 a + 1 = 0 and a is not equal to 0, find :**

**(i) a + 1 / a (ii) a ^{ 2} + 1 / a ^{ 2 }**

**Solution :**

(i) **a ^{ 2 } - 5 a + 1** = 0

=> a ^{ 2 } / a - 5 a / a + 1 / a = 0 [Dividing each term by a]

=> a - 5 + 1 / a = 0

=> **a + 1 / a = 5**

(ii) **a ^{ 2 } + 1 / a ^{ 2 }** = (a + 1 / a)

^{ 2 }- 2 = 5

^{ 2 }- 2 = 25 - 2 =

**23**