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# x(1-f) Equals: A) 1, B) Less Than, 1 C) More Than 1, D) Between 1 And 2

Sujoy Das
07/02/2018 0 0

Question:

If x = (9 + 4rt(5))^48 = [x] + f, where [x] is integral part of x and f is a fraction, then x(1-f) equals:

a) 1 b) less than 1 c) more than 1 d) between 1 and 2.

Method:

Take y = (9 - 4rt(5))^48 ; 0 < y < 1

=> xy = 1 and x+y = Integer

x + y = [x] + 1

[x] + f + y = [x] + 1

y = 1 - f

So x(1-f) = xy = 1

0 < y < 1

And x + y = Integer

When you add x + y,  integer that would come would be [x] + 1.

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