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Let ( 5 + 2 sqrt(6))^(n) = I + f , wher...

Let `( 5 + 2 sqrt(6))^(n) = I + f ` , where n, ` I in N ` and ` 0 lt f lt 1`, then
the value of ` f^(2) - f + I * f - I ` . Is

A

a natural number

B

a negative integer

C

a prime number

D

are irrational number

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `f^(2)-f+pf-p`
`=-f(1-f)-p(1-f)`
`=-[(p+f)(1-f)]`
where `p+f=(5+2sqrt(6))^(n)`
and `1-f=f'=(5-2sqrt(6))^(n)`
hence `f^(2)-f+pf-p=-1`
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