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

Explanation

To solve the equation \((x)[x] = 1\), where \([x]\) is the integral part of \(x\) and \((x)\) is the nearest integer to \(x\), we will analyze two cases: when \(x\) is an integer and when \(x\) is not an integer.

### Step 1: Case when \(x\) is an integer

1. If \(x\) is an integer, then \((x) = [x] = x\).
2. Substitute into the equation:
\[
x \cdot x = 1 \implies x^2 = 1
...