SOLUTION: Find two consecutive positive intergers such that the sum of their square is 85 This problem has confused me by adding in square, how do I go about solving this type of problem?

Question 65708: Find two consecutive positive intergers such that the sum of their square is 85
This problem has confused me by adding in square, how do I go about solving this type of problem?

Found 2 solutions by Nate, funmath:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
First Integer = i
Second Integer = i + 1
(i)^2 + (i + 1)^2 = 85
i^2 + i^2 + 2i + 1 = 85
2i^2 + 2i = 84
i^2 + i = 42
(i + 0.5)^2 = 42.25
i = -0.5 +- 6.5
i = -7 or i = 6
6 and 7
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Find two consecutive positive intergers such that the sum of their square is 85
Let the first integer be: x
Then the next consecutive integer is: x+1
Sum means add.
Square means raise to the second power
is means =.

(x+7)(x-6)=0
x+7=0 or x-6=0
x+7-7=0-7 or x-6+6=0+6
x=-7 or x=6
Since you were asked for two consecutive POSITIVE integers
The first integer is: x=6
and the second is: x+1=6+1=7
:
Sanity check:
are 6 and 7 consecutive integers? Yes!
Do the sum of their squares=85?
6^2+7^2=85
36+49=85
85=85 Yes!
It appears that we're sane...for now.
Happy Calculating!!!
RELATED QUESTIONS
Find two consecutive positive intergers such that the sum of their square is 85. (answered by checkley71)
Find two consecutive positive intergers such that the sum of their square is 85. Thank... (answered by checkley71)
Number Problem. Find two consecutive positive integers such that the sum of their square... (answered by timmy1729,bucky)
Please help me solve this problem: Find two consecutive positive integers such that the... (answered by Annabelle1)
Find two consecutive positive integers such that the sum of their square is... (answered by stanbon)
find two consecutive positive integers such that the sum of their square is... (answered by stanbon)
find two consecutive positive integers such that the sum of their square is... (answered by checkley75)
what are 2 consecutive positive intergers such that the sum of their squares is... (answered by Cintchr)
Please help me with this one... Number problems. Find two consecutive positive... (answered by checkley71)