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Popular Word Problems >

the sum of the squares of three consecutive odd numbers is 531. What are 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 o dd n u mb ers i s 531. Wha t a re t h e n u mb ers .

Solution

The numbers : \frac{- 6 + 1569}{3}, \frac{- 6 + 1569}{3} + 2, \frac{- 6 + 1569}{3} + 4 or - \frac{6 + 1569}{3}, - \frac{6 + 1569}{3} + 2, - \frac{6 + 1569}{3} + 4

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number 1 : x + 2

Consecutive number 2 : x + 4

A.T.Q.:

x^{2} + (x + 2)^{2} + (x + 4)^{2} = 531

Solve

x^{2} + (x + 2)^{2} + (x + 4)^{2} = 531 : x = \frac{- 6 + 1569}{3}, x = - \frac{6 + 1569}{3}

Plug in

x = \frac{- 6 + 1569}{3} : \frac{- 6 + 1569}{3} + 2, \frac{- 6 + 1569}{3} + 4

Plug in

x = - \frac{6 + 1569}{3} : - \frac{6 + 1569}{3} + 2, - \frac{6 + 1569}{3} + 4

The numbers : \frac{- 6 + 1569}{3}, \frac{- 6 + 1569}{3} + 2, \frac{- 6 + 1569}{3} + 4 or - \frac{6 + 1569}{3}, - \frac{6 + 1569}{3} + 2, - \frac{6 + 1569}{3} + 4

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