Question

If a = 9 - 4√5 , find the value of a²-1/a²

Answer 1

a=9-4√5
1/a=1/(9-4√5)
=9+4√5/(9)^2 - (4√5)^2
=9+4√5/(81-80)
=9+4√5
a^2 -(1/a)^2=[(9-4√5)^2]-[(9+4√5)^2]
=81+80-72√5-(81+80+72√5)
=81+80-72√5-81-80-72√5

80 and 81 gets cancelled
=(-72-72)√5
= -144√5

Answer 2

Answer:

322

Step-by-step explanation:

If a =9-4√5 , find the value of a²+1/a²

a = 9-4√5

1/a = 1/ (9 - 4√5)  

= (9 + 4√5) /((9 - 4√5)(9 + 4√5) )

=    (9 + 4√5) /(81 - 80)

= (9 + 4√5)

a²+1/a² = (a + 1/a)² - 2a(1/a)

= ( 9 - 4√5 + 9 + 4√5)² - 2

= 18² - 2

= 324 - 2

= 322

or

a²+1/a² = (a - 1/a)² + 2a(1/a)

= ( 9 - 4√5 - 9 - 4√5)² + 2

= (-8√5)² + 2

= 320 + 2

= 322