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Question

if a not=0 and a-1/a=3 find

(i) a2+1/a2

(ii) a3-1/a3

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Solution

Answer :

Given a 0 And

a - 1a = 3 --------------- ( 1 )

i ) Find value of : a2 + 1a2


Squaring equation 1 , we get

( a - 1a )2 = 32

a2 + 1a2 - 2 ( a ) ( 1a ) = 9 [ As we know ( a + b )2 = a2 + b2 + 2ab ]

a2 + 1a2 - 2 = 9

a2 + 1a2 = 9 + 2

a2 + 1a2 = 11 ( Ans )


ii ) Find value of : a3 - 1a3
Now taking Cube of equation 1 , we get

( a - 1a )3 = 33

a3 - 1a3 - 3 ( a ) ( 1a ) ( a - 1a ) = 27 [ As we know ( a - b )3 = a3 - b3 - 3ab( a - b ) ]

a3 - 1a3 ​- 3 ( 3 ) = 27 ( Given ​a - 1a = 3 ​ )

a3 - 1a3 - 9 = 27

a3 - 1a3 = 27 + 9

a3 - 1a3 = 36 ( Ans )

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