SOLUTION: How do we solve the following problem using factorization? The sum of the squares of two consecutive integers is 13 Find the integers.

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Question 376333: How do we solve the following problem using factorization?
The sum of the squares of two consecutive integers is 13 Find the integers.
Found 2 solutions by robertb, jim_thompson5910:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
If 1,2 then sum of squares is 5.
If 2,3 then the sum of squares is 13, bulls-eye! Also -2, -3 will work.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of the squares of two consecutive integers is 13" means that x%5E2%2B%28x%2B1%29%5E2=13


x%5E2%2B%28x%2B1%29%5E2=13 Start with the given equation.


x%5E2%2Bx%5E2%2B2x%2B1=13 FOIL


x%5E2%2Bx%5E2%2B2x%2B1-13=0 Subtract 13 from both sides.


2x%5E2%2B2x-12=0 Combine like terms.


2%28x%5E2%2Bx-6%29=0 Factor out the GCF 2


2%28x%2B3%29%28x-2%29=0 Factor x%5E2%2Bx-6 to get %28x%2B3%29%28x-2%29


x%2B3=0 or x-2=0 Use the zero product property


x=-3 or x=2 Solve for x.


So if x=2, then x%2B1=2%2B1=3 making the two numbers to be 2 and 3. Notice how 2%5E2%2B3%5E2=4%2B9=13


Or, if x=-3, then x%2B1=-3%2B1=-2 making the two numbers to be -3 and 2. Notice how %28-3%29%5E2%2B%28-2%29%5E2=9%2B4=13


So the two numbers are

2 and 3

OR

-3 and -2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim