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

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Answer 1 · 2016-02-21T20:13:21

-15 and -17

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)

$n+2=-15$