Question

The difference of the squares of two consecutive numbers is their sum.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let two consecutive numbers be x and (x + 1).

Then squares of these numbers are x² and (x + 1)².

Difference of squares of these consecutive numbers = (x + 1)² – x²

= x² + 1 + 2x – x²  ...[∵ (a + b)² = a² + b² + 2ab)

= 2x + 1

= x + x + 1

= (x) + (x + 1)

= Sum of the two consecutive numbers x and x + 1

Thus, difference of squares of two consecutive numbers = sum of the same consecutive numbers.