Home » Ask & Discuss » Mathematics. » Algebra « Back to Discussion

Algebra

Forum Expert

Joined:	28 Feb 2007
Post:	2173

17 Jan 2008 19:50:19 IST

0 People liked this

891

Nice one

None

= (n +

(n²- 4))/2 where n is an integer

then prove that

^m = (k+

(k²-4))/2 where k,m are natural numbers.

Share this article on:

Comments (11)

Sairam

Blazing goIITian

Joined: 14 Sep 2007

Posts: 573

17 Jan 2008 21:47:29 IST

Like 1 people liked this

hs bhatt,

the gvn eqn implies

is aroot of x^2-nx+1

now to get da eqn whose roots are mth powers of orign eqn, raise x to xpower 1/m

so x^2/m - nx^1/m+1=0 has alpha power m as the roots

and the roots of dis eqn are also of d form k+sqrt(k^2-4)/2

Hari Shankar

Forum Expert

Joined: 28 Feb 2007

Posts: 2173

18 Jan 2008 09:31:55 IST

Like 1 people liked this

You are only proving that (

^m)^1/m= (n+

(n²-4))/2 =

. We are back to square one.

We should be looking at x^2m- nx^m+1 = 0.

Abhijith

Blazing goIITian

Joined: 23 Jan 2007

Posts: 678

18 Jan 2008 16:14:56 IST

Like 2 people liked this

Nice one indeed hsbhatt,

Ok first things first. The condition

should be true.

Let

be defined as above. Then,

Fact: for any positive integer

, the number

is a positive integer.

Proof by induction on

we have

Thus

Now on, binomial expansion of the LHS and induction completes the proof.

Let

by above Fact,

is a positive integer.

Since

, we get:

Hari Shankar

Forum Expert

Joined: 28 Feb 2007

Posts: 2173

18 Jan 2008 18:23:14 IST

Like 1 people liked this

The working's fine.

Except that n>=2 need not hold.

You could use induction as follows

Assume

^m + 1/

^m = p (an integer)

Then

^(m+1) + 1/

^(m+1) = (

^m + 1/

^m) (

+1/

) - ((

^(m-1) + 1/

^(m-1))

= an integer.

Its a little easier to understand.

By the way, if you are an IIT aspirant, your chances of getting in are pretty good.

Abhijith

Blazing goIITian

Joined: 23 Jan 2007

Posts: 678

18 Jan 2008 18:59:27 IST

Like 0 people liked this

why do u say

need to be true? Wont

become complex otherwise?

yes i am an iit aspirant..12th std student..thanks a lot! i do hope i make it...

Hari Shankar

Forum Expert

Joined: 28 Feb 2007

Posts: 2173

18 Jan 2008 21:40:49 IST

Like 1 people liked this

can be complex no harm. Just go through each step of the soln and see if

being complex is any hindrance.

U r sure to get IIT man. If you were stock, I would buy you for sure! Just make sure you pay this much attention to Phy and Chem too. They r just as imp.

Abhijith

Blazing goIITian

Joined: 23 Jan 2007

Posts: 678

19 Jan 2008 13:55:30 IST

Like 0 people liked this

oh ok... and thanks for saying that!!! i'll hav to work on chem...

pooja agnihotri

New kid on the Block

Joined: 12 Jan 2008

Posts: 13

19 Jan 2008 18:32:03 IST

Like 0 people liked this

konichiwa2x nice solun cheers

Abhijith

Blazing goIITian

Joined: 23 Jan 2007

Posts: 678

20 Jan 2008 19:17:01 IST

Like 0 people liked this

thanks sizzle!

abhishek gupta

Blazing goIITian

Joined: 30 Sep 2007

Posts: 361

15 Mar 2008 23:29:54 IST

Like 0 people liked this

konichiwa2x (1302)

Abhijith

Blazing goIITian

Joined: 23 Jan 2007

Posts: 678

16 Mar 2008 01:01:44 IST

Like 0 people liked this

well, why did u bring up this old post now?

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team