Expansions-9
From Homeworkwiki
If a 2 + 1 / a 2 = 23 , find the value of a 3 + 1 / a 3
Solution :
a 2 + 1 / a 2 = 23
=> a 2 + 1 / a 2 + 2 = 23 + 2 = 25
=> ( a + 1 / a ) 2 = 25
=> ( a + 1 / a ) = ± 5
When a + 1 / a = 5 :
a 3 + 1 / a 3 = ( a + 1 / a ) 3 - 3 ( a + 1 / a )
= ( 5 ) 3 - 3 X 5
= 110
When a + 1 / a = - 5 :
a 3 + 1 / a 3 = ( a + 1 / a ) 3 - 3 ( a + 1 / a )
= ( - 5 ) 3 - 3 X ( - 5 ) = - 125 + 15
= - 110
