Question

Complete solution set of the inequation {n} ({n} – 1) ({n} + 2) ≥ 0 (where {·} denotes fractional part function) is​

Answer 1

Given :  {n} ({n} – 1) ({n} + 2) ≥ 0      

To Find : Value of n

Solution:

{n} ({n} – 1) ({n} + 2) ≥ 0

0 ≤ {n}  < 1

=> {n} – 1  =  -1  ≤ {n}  < 0

{n} + 2  = 2 ≤ {n}  < 3

{n}  is non negative

{n} + 2  is non negative

{n} – 1 is always negative

Hence result will be non Positive

inequality will hold true only if  {n}  = 0  

Hence All integers

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