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 check if they can be expressed in the standard form of a quadratic equation, which is \(Ax^2 + Bx + C = 0\), where \(A\), \(B\), and \(C\) are constants and \(A \neq 0\).

Let's analyze each equation step by step.

### (i) \( (x-2)^2 + 1 = 2x - 3 \)

1. **Expand the left side**:
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