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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.
Answer:
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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