Question

If a=9-4√5 find the value of a-1/a

Answer 1

Answer:

a-1/a = -8√5

Explanation:

a = 9 - 4√5 -----( 1 )

1/a = 1/(9-4√5)

= (9+4√5)/[(9-4√5)(9+4√5)]

= (9+4√5)/[9²-(4√5)²]

= (9+4√5)/(81-80)

= 9+4√5 ----( 2 )

Now,

a-1/a

= 9-4√5-(9+4√5)

= 9-4√5-9-4√5

= 2(-4√5)

= -8√5

Therefore,

a-1/a = -8√5

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