x and y are positive integers satisfying 0 < x - 3y < 1 and b is the d

­I used reasoning in this question. 

If \((x - \sqrt{3}y) \) is a +ve decimal number without any integer value (the expression is greater than 0 and less than 1), and x and y are integers (given) then:

Fact 1: Integer +/- Integer = integer 
Fact 2: Integer +/- (irrational number)*(Integer) = Integer with decimal value. This is what we are dealing with here.

Now b is the decimal value of \((x+ \sqrt{3}y)\). So if the answer is 1.234 of this expression then 1 would come from integer x, and 0.234 would come from \(\sqrt{3}\)y.  [Property used: Integer + (irrational number)*(Integer)]

So if I have to express it in terms of b, it would be 1 + 0.234 or 1 + b. 

Similarly, for \((x - \sqrt{3}y)^3\). It will be expressed as 1 - b. Or decimal value (here resulted by multiplication of \(\sqrt{3}\) with integer y) is being subtracted from an integer value (here represented by variable x). [Property used: Integer - (irrational number)*(Integer)]. 

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PS: analyse it yourself. Don't just trust me­­­­­­­­­­