SOLUTION: I cannot get anywhere with this problem, please help. Find two consecutive positive integers such that the sum of their squares is 85.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I cannot get anywhere with this problem, please help. Find two consecutive positive integers such that the sum of their squares is 85.      Log On


   



Question 107282: I cannot get anywhere with this problem, please help.
Find two consecutive positive integers such that the sum of their squares is 85.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If consecutive integers starting at n, then their sum could be written as
n+%2B+%28n%2B1%29+%2B+%28n%2B2%29+%2B...%2B+%28n%2Bk-1%29+
since you have two consecutive integers, you weill use
n+%2B+%28n+%2B+1%29
to find two consecutive positive integers such that the+sum+of their+squares is 85, you will have:
n%5E2+%2B+%28n+%2B+1%29%5E2+=+85
n%5E2+%2B+n%5E2+%2B+2n+%2B+1+=+85
2n%5E2+%2B+2n+=+85+-+1
2%28n%5E2+%2B+n%29+=+84.........divide both sides by 2
n%5E2+%2B+n+=+42
or
n%5E2+%2B+n+-+42+=+0....writen in the standard form .....so you can apply quadratic formula to find n%5B1%2C2%5D, and use only n+%3E+0

n%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281%5E2+-4%2A1%2A%28-42%29+%29%29+%2F+%282%2A1%29
n%5B1%2C2%5D=%28-1+%2B-+sqrt+%281+%2B+168+%29%29+%2F+%282%29
n%5B1%2C2%5D=%28-1+%2B-+sqrt+%28169%29%29+%2F+%282%29
n%5B1%2C2%5D=%28-1+%2B-+13%29+%2F+%282%29
n%5B1%5D=%28-1+%2B+13%29+%2F+%282%29....you will need just this one because n will be positive number
n%5B1%5D=%28+12%29+%2F+%282%29

n%5B1%5D=+6+........this is first number
next consecutive number will be 7
now check if the sum of their squares is +85
6%5E2+%2B+7%5E2+=+36+%2B+49+=+85