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Solve (x)2 = [x]2 + 2x Where [x] represents greatest integer less than or equal to x. (x) represents integer just greater than or equal to x

Solve (x)2 = [x]2 + 2x
Where [x] represents greatest integer less than or equal to x.
(x) represents integer just greater than or equal to x

Grade:Select Grade

1 Answers

Hasan Naqvi
97 Points
6 years ago
if x is not an integer, then [x] = (x)-1
(x)=[x]+1
(x) = {[x]+1}2
= [x]2 + 2[x] + 1 = [x]2 + 2x(acc to question)
 
ie 2[x]+1= 2x
ie x-[x] = 0.5
 
so x belongs to {..., -1.5, -0.5, 0.5, 1.5, 2.5, ...}
 
If x is an integer, then [x]=(x), and the eqn is satisfied for x= 0
 
so x belongs to  {..., -1.5, -0.5, 0, 0.5, 1.5, 2.5, ...}

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