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Popular Word Problems >

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

Solution

prove

a l g e b r ai c a ll y t ha t t h e d i ff ere n ce b e tw ee n t h e s q u a res o f an y tw o co n sec u t i v e in t e g ers i s e q u a l t o t h e s u m o f t h ese tw o in t e g ers .

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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