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

1 Answer
Feb 21, 2016

-15 and -17

Explanation:

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

The sum of squares=514:

n^2+(n+2)^2=514n2+(n+2)2=514

n^2+n^2+4n +4=514n2+n2+4n+4=514

2n^2+4n -510=02n2+4n510=0

n=(-4+-sqrt(4^2-4*2*(-510)))/(2*2)n=4±4242(510)22

n=(-4+-sqrt(16+4080))/4n=4±16+40804

n=(-4+-sqrt(4096))/4n=4±40964

n=(-4+-64)/4n=4±644

n=-68/4=-17n=684=17 (because we want a negative number)

n+2=-15n+2=15