Question

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

• A. True
• B. False

Answer 1

The correct option is A True

Let two consecutive numbers be 100 and 101.
The difference of the squares of two consecutive numbers,
= $(101{)}^2-(100{)}^2$
Using the identity, $(a{)}^2-(b{)}^2=(a+b)(a-b)$
$=(101+100)(101-100)=201\left(1\right)=201$.
The sum of two consecutive numbers $=100+101=201$
Hence, The difference of the squares of two consecutive numbers is equal to their sum.