If `[x]` and `(x)` are the integral part of x and nearest integer to `x` then solve `(x)[x]=1`

Explanation

CaseI If `x epsilonI`, then `x=[x]=(x)`
`:.` Given equation convert in `x^(2)=1`
`:.x=(+-1)`
Case II If `x!inI` then `(x)=[x]+1`
`:.` Given equation convert in
`([x]+1)[x]=1implies[x]^(2)+[x]-1=0`
or `[x]=(-1+-sqrt(5))/2` [impossible]
Then final answer is `x=+-1`.