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

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) (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) (Show Source): You can put this solution on YOUR website!
"The sum of the squares of two consecutive integers is 13" means that

Start with the given equation.

FOIL

Subtract 13 from both sides.

Combine like terms.

Factor out the GCF 2

Factor to get

or Use the zero product property

or Solve for x.

So if , then making the two numbers to be 2 and 3. Notice how

Or, if , then making the two numbers to be -3 and 2. Notice how

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
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