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

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Question 115425: Find two consecutive positive integers such that the sum of their squares is 85.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You are off to a good start, but have some errors in your work

x%5E2%2B%28x%2B1%29%5E2=85 You have the correct equation. So let's start there


x%5E2%2Bx%5E2%2B2x%2B1=85 Foil


x%5E2%2Bx%5E2%2B2x%2B1-85=0 Subtract 85 from both sides


2x%5E2%2B2x-84=0 Combine like terms


2%28x%2B7%29%28x-6%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B7=0 or x-6=0

x=-7 or x=6 Now solve for x in each case


So our answer is
x=-7 or x=6


So if x=-7 , then the first number is -7. Now let's find the second number

-7%2B1=-6

So the second number is -6

So one pair of numbers is -7, -6

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Now if x=6 , then the first number is 6. Now let's find the second number

6%2B1=7

So the second number is 7

So another pair of numbers is 6,7

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Answer:

This means the two numbers are either 6, 7 OR the two numbers -7,-6