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
