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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.

Solución

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

Solución

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

Pasos de solución

Represent the numbers with

x

:

First number : x

Consecutive number : x + 1

A.T.Q.:

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

Resolver

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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