Math problem...

[zippy]

My math teacher gave us this problem to do as extra credit:

Show that the sum of 1 and the product of any four consecutive integers is a perfect square.

Here is what I did:

1+(x)(x+1)(x+2)(x+3)
.
.
.
.
x^4+6x^3+11x^2+6x+1

Now what? /me scratches head

I know it works...I tried it with some numbers, plugged them in, works great (pretty cool really). I just don't know how I can show that the mess I came out with will always be a perfect square.

Lil help...

Thanks guys!

 

[gopunk]

factor it, to show that it's in the form of (ax+b)^2

 

[HardcoreRobot]

Sounds like a situation for a good ole proof by induction. And no, I dont know how to do it, I sucked in that logic class!

 

[zippy]

Ah, got it, that equation scared me at first I guess...but it was actually rather easy to factor.

(x^2+3x+1)^2

Hooray!

Thanks for the help...ya punk. hehe, sorry, that was a bad pun

 

[zippy]

<< good ole proof by induction. >>

Huh? Ummm...this is precalc class...maybe induction is in Calc?

 

[gopunk]

np zippy.

info on proof by induction (long read)

 

[Ameesh]

you dont need induction to to do this, his factoring methos is just fine.

 

[gopunk]

yea i know, i was just giving him the link just for reading.

 

[eLiu]

yea...the factoring method is pretty straightforward here, u dont need any fancy math to do it