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If (3√3 + 5) ^ 2n + 1 = p + f, where p is an integer and f is a real fraction, then f (p + f) is equal?

If (3√3 + 5) ^ 2n + 1 = p + f, where p is an integer and f is a real fraction, then f (p + f) is equal?

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
Let (3√3 - 5) ^ 2n + 1 = F where F lies in between 0 and 1.
we are given that (3√3 + 5) ^ 2n + 1 = p+f
subtracting
p+f-F= 2*integer ( we have used binomial expansion here)
So f-F is an integer but f-F lies in -1 to 1. The only integral value iin between them is 0. So f-F= 0 or f= F
Multiplying both eqns we have
F(p+f)= 2^(2n+1)
Or f(p+f) = 2^(2n+1)
 

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