If `{x}` and `[x]` represent fractional and integral part of `x` respectively then solve the equation `x-1=(x-[x])(x-{x})`

Explanation

To solve the equation \( x - 1 = (x - [x])(x - \{x\}) \), where \([x]\) is the integral part of \(x\) and \(\{x\}\) is the fractional part of \(x\), we can follow these steps:

### Step 1: Understand the Definitions
Recall that:
- \( x = [x] + \{x\} \)
- \([x]\) is the greatest integer less than or equal to \(x\)
- \(\{x\} = x - [x]\) is the fractional part of \(x\), satisfying \(0 \leq \{x\} < 1\)

...