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Popular Word Problems >

The sum of the squares of three consecutive integers is 110. Find the numbers

Solution

T h e s u m o f t h e s q u a res o f t h ree co n sec u t i v e in t e g ers i s 110. F in d t h e n u mb ers

Solution

The numbers : 5, 6, 7 or - 7, - 6, - 5

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number 1 : x + 1

Consecutive number 2 : x + 2

A.T.Q.:

x^{2} + (x + 1)^{2} + (x + 2)^{2} = 110

Solve

x^{2} + (x + 1)^{2} + (x + 2)^{2} = 110 : x = 5, x = - 7

Plug in

x = 5 : 6, 7

Plug in

x = - 7 : - 6, - 5

The numbers : 5, 6, 7 or - 7, - 6, - 5

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