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in Differential equations by (64.8k points)

Prove that [2x] = [x] + [x + 1/2]

1 Answer

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Best answer

Case-I: When x is integer 

i.e x = n

L.H.S = [2n] = 2n

R.H.S = [n] + [n + 1/2] = n + n = 2n

Case-II: when x is not an integer.  

i.e. x = n + f, where 0  f < 1 

 L.H.S = [2(n + f)] = 2n + [2 f]

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