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Popular >

the sum of the squares of three consecutive odd numbers is 531. What are the numbers.

Solution

the sum of the squares of three consecutive odd numbers is 531. What are the numbers.

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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