SOLUTION: Find two consecutive positive integers such that the sum of their squares is 85.

Question 18475: Find two consecutive positive integers such that the sum of their squares is 85.
Answer by xcentaur(357) (Show Source): You can put this solution on YOUR website!
Let the first positive integer be x
Then the second positive integer will be (x+1)

Given that the sum of their squares is 85,we get:
x^2 + (x+1)^2 = 85
x^2 + x^2 + 1 + 2x = 85
2x^2 + 2x = 85-1
2(x^2+x)=84
2(x^2+x)=2(42)
x^2+x=42
x^2+x-42=0
x^2-6x+7x-42=0
(x-6)(x+7)=0
x=6,-7
We require positive integers hence x cannot be -7
therefore,x=6

first number=6
second number=7

Hope this helps,
Prabhat

RELATED QUESTIONS
Find two consecutive positive integers such that the sum of their squares is... (answered by Nate)

Find two consecutive positive integers such that the sum of their squares is... (answered by checkley71)

Number problems. Find two consecutive positive integers such that the sum of their... (answered by checkley75)

Find two consecutive positive integers such that the sum of their squares is 85. Thank (answered by Nate)

Number problems. Find two consecutive positive integers such that the sum of their... (answered by jim_thompson5910)

Number problems. Find two consecutive positive integers such that the sum of their... (answered by Adam,bucky)

Find two consecutive positive integers such that the sum of their squares is 85. (answered by jim_thompson5910)

Find two consecutive positive integers such that the sum of their squares is... (answered by jim_thompson5910)

Number problems. Find two consecutive positive integers such that the sum of their... (answered by ganesh)