SOLUTION: Find two consecutive positive integers such that the sum of their squares is 85. Can anyone tell me if I'm right? I am coming up with 6 and 7 - is this correct? Thanks!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find two consecutive positive integers such that the sum of their squares is 85. Can anyone tell me if I'm right? I am coming up with 6 and 7 - is this correct? Thanks!      Log On


   

Question 41403: Find two consecutive positive integers such that the sum of their squares is 85. Can anyone tell me if I'm right?
I am coming up with 6 and 7 - is this correct?
Thanks!
Answer by rajagopalan(174) About Me  (Show Source):
You can put this solution on YOUR website!
you are absolutely right.
let first number be x
let next number be x+1
sum of squars of these 2 = x^2+x^2+2x+1 = 85
2x^2+2x+1=85
2x^2+2x =85-1
2x^2+2x =84
divide by 2 thro out
x^2+x=42
x^2+x-42=0
x^2+7x-6x-42=0
x(x+7)-6(x+7)=0
(x-6)(x+7)=0
x=6 0r -7
deleting negative answer
we get the numbers as 6 and 7.
cheers