Which of the following is a quadratic equation?

1. x² + 1 = (2 - x)² + 3

2. 2x² + 3 = (5 + x)(2x - 3)

3. x³ - x² = (x - 1)³

4. none of these

Solving,

⇒ x³ - x² = (x - 1)³

⇒ x³ - x² = [(x)³ - (1)³ - 3x × 1 × (x - 1)]

⇒ x³ - x² = x³ - 1 - 3x(x - 1)

⇒ x³ - x² = x³ - 1 - 3x² + 3x

⇒ x³ - x² - x³ + 1 + 3x² - 3x = 0

⇒ x³ - x³ - x² + 3x² - 3x + 1 = 0

⇒ 2x² - 3x + 1 = 0

The highest power of equation is 2 and it's equivalent to ax² + bx + c = 0 . Hence the equation is a quadratic equation.

Hence, option 3 is the correct option.