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anonymous
 one year ago
Medal & Fan.
The sum of the squares of 3 consecutive positive integers is 116. What are the numbers?
Which of the following equations is used in the process of solving this problem?
3n^2 + 5 = 116
3n^2 + 3n + 3 = 116
3n^2 + 6n + 5 = 116
anonymous
 one year ago
Medal & Fan. The sum of the squares of 3 consecutive positive integers is 116. What are the numbers? Which of the following equations is used in the process of solving this problem? 3n^2 + 5 = 116 3n^2 + 3n + 3 = 116 3n^2 + 6n + 5 = 116

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1an and example of 3 consecutive positive integers is: 1,2,3 or 3,4,5 ... or (n1),n,(n+1) we don't know what they are so let's go with the (n1),n,(n+1) being the 3 consecutive positive integers so you have the sum of the squares of them is 116 that is (n1)^2+n^2+(n+1)^2=116 play with the left hand side

hybrik
 one year ago
Best ResponseYou've already chosen the best response.0Freckles can do this one, I have to do something at the moment, be right back.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0probly horribly wrong

freckles
 one year ago
Best ResponseYou've already chosen the best response.1(n1)^2 = (n1)(n1) do you know how to expand this?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yeah or it is just really distributing like n(n1)1(n1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1right and we can also expand (n+1)^2 in a similar way

freckles
 one year ago
Best ResponseYou've already chosen the best response.1which should be n^2+2n+1 for (n+1)^2 so you have this now: \[(n1)^2+n^2+(n+1)^2 =116 \\ (n^22n+1)+n^2+(n^2+2n+1)=116 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1combine like terms on the left hand side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[2n ^{2}+1+n^2 +2n^2+1=116\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1don't go any further with what you have just wrote

freckles
 one year ago
Best ResponseYou've already chosen the best response.1in the equation I wrote how many n^2 's do you see?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1now let's look at the n's you have 2n+2n which equals ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if someone gave you 3 apples and your three all 3 apples away how many apples do you have left?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if someone gave you 3 apples and your threw all 3 apples away how many apples do you have left?* yes 0

freckles
 one year ago
Best ResponseYou've already chosen the best response.10 also replace 2n with 5 you have 5+5 and we know that is 0 you can also write this 2n+2n both terms have a common factor n factor the n out n(2+2) but you should know 2+2=0 so you have n(0) but 0 times anything will result in 0 so n(0)=0 so 2n+2n=0

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the last thing to add are the constant terms (the terms with out any variable)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1can you show me what you think you have?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1sure why not you probably want me to check the whole thing right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yep but that doesn't match any of your answers I guess they chose their 3 consecutive numbers differently maybe they chose n,n+1,n+2 which also works \[n^2+(n+1)^2+(n+2)^2=116 \\ n^2+n^2+2n+1+n^2+4n+4=116 \\ 3n^2+6n+5=116 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can choose the three consecutive integers in many ways

freckles
 one year ago
Best ResponseYou've already chosen the best response.1that is solving either one of the equations will result in the same 3 consecutive integers

freckles
 one year ago
Best ResponseYou've already chosen the best response.1though I like my equation better because it seems simpler to solve :p
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