Question

Prove: The difference of the squares of two successful integers is equal to the sum of the integers.

Answer 1

Given,

The difference of the squares of two successful integers is equal to the sum of the integers.

Required

Prove of the given statement.

Consider,

n and n+1 are two consecutive integers.

According to the statement,

`\begin{gathered} (n+1)^2-n^2=n^2+2n+1-n^2 \\ =2n+1 \\ =n+n+1 \\ =n+(n+1) \end{gathered}`

Hence,

it is proved.