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Popular >

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

Solución

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

Solución

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

Pasos de solución

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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