Question

The sum of the squares of two consecutive negative odd integers is equal to 514. How do you find the two integers?

Answer 1

-15 and -17

Explanation:

Two odd negative numbers: `n` and `n+2`.

The sum of squares=514:

`n^2+(n+2)^2=514`

`n^2+n^2+4n +4=514`

`2n^2+4n -510=0`

`n=(-4+-sqrt(4^2-4*2*(-510)))/(2*2)`

`n=(-4+-sqrt(16+4080))/4`

`n=(-4+-sqrt(4096))/4`

`n=(-4+-64)/4`

`n=-68/4=-17` (because we want a negative number)

`n+2=-15`