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The sum of the squares of two consecutive positive integers is 85 . Find the numbers.

Solution

The sum of the squares of two consecutive positive integers is 85 . Find the numbers.

Solution

The numbers : 6, 7

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number : x + 1

A.T.Q.:

x^{2} + (x + 1)^{2} = 85

Solve

x^{2} + (x + 1)^{2} = 85 : x = 6, x = - 7

Select positive solutions:

6

x + 1 = 6 + 1 = 7

The numbers : 6, 7

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