Question

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

Answer 1

@hybrik

Answer 2

an and example of 3 consecutive positive integers is:
1,2,3
or
3,4,5
...
or
(n-1),n,(n+1)

we don't know what they are so let's go with the (n-1),n,(n+1) being the 3 consecutive positive integers
so you have the sum of the squares of them is 116
that is (n-1)^2+n^2+(n+1)^2=116
play with the left hand side

Answer 3

Freckles can do this one, I have to do something at the moment, be right back.

Answer 4

2n+2+n+2n+2=116?

Answer 5

probly horribly wrong

Answer 6

(n-1)^2
=
(n-1)(n-1)
do you know how to expand this?

Answer 7

foil maybe?

Answer 8

yeah
or it is just really distributing
like n(n-1)-1(n-1)

Answer 9

n^ 2- 2n + 1

Answer 10

right
and we can also expand (n+1)^2 in a similar way

Answer 11

which should be n^2+2n+1 for (n+1)^2

so you have this now:
\[(n-1)^2+n^2+(n+1)^2 =116 \\ (n^2-2n+1)+n^2+(n^2+2n+1)=116 \]

Answer 12

combine like terms on the left hand side

Answer 13

\[-2n ^{2}+1+n^2 +2n^2+1=116\]

Answer 14

not done yet

Answer 15

don't go any further with what you have just wrote

Answer 16

in the equation I wrote how many n^2 's do you see?

Answer 17

3

Answer 18

n^2+n^2+n^2 is 3n^2

Answer 19

now let's look at the n's
you have -2n+2n which equals ?

Answer 20

n

Answer 21

if someone gave you 3 apples and your three all 3 apples away how many apples do you have left?

Answer 22

0

Answer 23

if someone gave you 3 apples and your threw all 3 apples away how many apples do you have left?*
yes 0

Answer 24

so -2n+2n is ?

Answer 25

0

Answer 26

0 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

Answer 27

the last thing to add are the constant terms (the terms with out any variable)

Answer 28

can you show me what you think you have?

Answer 29

the whole thing?

Answer 30

sure why not
you probably want me to check the whole thing right?

Answer 31

3n^2+2=0?

Answer 32

yep 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
\[n^2+(n+1)^2+(n+2)^2=116 \\ n^2+n^2+2n+1+n^2+4n+4=116 \\ 3n^2+6n+5=116 \]

Answer 33

you can choose the three consecutive integers in many ways

Answer 34

that is solving either one of the equations will result in the same 3 consecutive integers

Answer 35

thanks again

Answer 36

though I like my equation better because it seems simpler to solve :p