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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?
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+fsubtractingp+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= FMultiplying both eqns we haveF(p+f)= 2^(2n+1)Or f(p+f) = 2^(2n+1)
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