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Popular Word Problems >

The sum of the squares of five consecutive positive integers starting with is 2655

Solução

T h e s u m o f t h e s q u a res o f f i v e co n sec u t i v e p os i t i v e in t e g ers s t a r t in g w i t h i s 2655

Solução

The numbers : 21, 22, 23, 24, 25

Passos da solução

Represent the numbers with

x

:

First number : x

Consecutive number 1 : x + 1

Consecutive number 2 : x + 2

Consecutive number 3 : x + 3

Consecutive number 4 : x + 4

A.T.Q.:

x^{2} + (x + 1)^{2} + (x + 2)^{2} + (x + 3)^{2} + (x + 4)^{2} = 2655

Resolver

x^{2} + (x + 1)^{2} + (x + 2)^{2} + (x + 3)^{2} + (x + 4)^{2} = 2655 : x = 21, x = - 25

Select positive solutions:

21

x + 1 = 21 + 1 = 22

x + 2 = 21 + 2 = 23

x + 3 = 21 + 3 = 24

x + 4 = 21 + 4 = 25

The numbers : 21, 22, 23, 24, 25

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