Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Show that =
{x} 2 – 
{x}, where {x} denotes the fractional part of x.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. We have, {x} = x –[x]
Let k ≤ x < k + 1, where k ∈ N. Then,
= 
= –
= 
+ 
– 
= 
+ 
– 
= 
+ 
– 
– 
= 
–kx + 
– 
= 
(x 2 – 2kx + k 2 ) + 
(k –x)
= 
(x – k) 2 – 
(x –k)
= 
(x – [x]) 2 – 
(x–[x])
= 
{x} 2 – 
{x}
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