Check whether the following are quadratic equations :
(i) `(x-2)^2+1=2x-3`
(ii) `x(x+1)+8=(x+2)(x-2)`
(iii) `x(2x+3)=x^2+1`
(iv) `(x+2)^3=x^3-4`

Explanation

To determine whether the given equations are quadratic equations, we need to simplify each equation and check if they can be expressed in the standard form of a quadratic equation, which is \( ax^2 + bx + c = 0 \), where \( a \neq 0 \).

### Step-by-Step Solution:

**(i)** Check if \( (x-2)^2 + 1 = 2x - 3 \) is a quadratic equation.

1. Expand the left side:
\[
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