SOLUTION: This is from a worksheet: Find two consecutive integers such that the sum of their squares is 85. I have getten this far: n^2+(n+1)^2=85 At some point I will have to divide

Question 88630: This is from a worksheet: Find two consecutive integers such that the sum of their squares is 85.
I have getten this far:
n^2+(n+1)^2=85
At some point I will have to divide each side by half?
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Foil

Subtract 85 from both sides

Combine like terms

Now let's use the quadratic formula to solve for n:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=2, and c=-84

Square 2 to get 4

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Check:
Plug in

Add

Square each number

Add. So this solution works

Plug in

Add

Square each number

Add. So this solution works

So we have 2 pairs of numbers

6 and 7
or
-7 and -6
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find two consecutive integers such that the sum of their squares is 85.
I have gotten this far:
n^2 + (n+1)^2 = 85
:
to continue, FOIL (n+1)(n+1)
n^2 + (n^2 + 2n + 1) = 85
:
n^2 + n^2 + 2n + 1 - 85 = 0: subtract 85 from both sides:
:
2n^2 + 2n - 84 = 0; combine like terms, you have a quadratic equation
:
n^2 + n - 42 = 0; simplify, divide equation (each term) by 2
:
(n+7)(n-6) = 0; factors easily:
:
n = -7
and
n = +6
:
Both these solutions will work, here's x = -7
(-7^2) + (-6^2) =
+49 + 36 = 85
:
:
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