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Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

Solution

Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

Solution

The numbers : - \frac{1}{2}, \frac{1}{2}

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number : x + 1

A.T.Q.:

x^{2} - (x + 1)^{2} = x + x + 1

Solve

x^{2} - (x + 1)^{2} = x + x + 1 : x = - \frac{1}{2}

x + 1 = - \frac{1}{2} + 1 = \frac{1}{2}

The numbers : - \frac{1}{2}, \frac{1}{2}

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