SOLUTION: the sum of the squares of six consecutive integers is 1111. what are the integers and what is the problem solving strategy?

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Question 166360: the sum of the squares of six consecutive integers is 1111. what are the integers and what is the problem solving strategy?
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Consecutive integers follow the pattern: x, x+1, x+2, x+3...

Since the "sum of the squares of six consecutive integers is 1111", this means that


Now FOIL the expressions to get




and combine like terms to get





I'll let you solve the equation.


Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!
the sum of the squares of six consecutive integers is 1111. what are the integers and what is the problem solving strategy?

Let consecutive the integers be , , , , , and 

Then we have the equation:







Collect terms:




 
Divide through by 6:



Factor:



Use the zero factor property:



So there are two solutions:

If ,  then the consecutive integers are

, , , , , and 

or

, , , , , and 

or

, , , , , and 

and if ,  then the consecutive integers are

, , , , , and 

or

, , , , , and 

or

, , , , , and 

Edwin
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