Home » Ask & Discuss » Mathematics
« Back to Discussion

Algebra

Blazing goIITian

Joined:	28 Apr 2009
Post:	997

23 Jun 2009 11:47:53 IST

0 People liked this

1273

8th class question

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

Unit Fractions

Find natural numbers x,y,z such that

where

YOu may be surprised at just how many solutions exist.

Comments (23)

Go to Page...

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

23 Jun 2009 11:49:03 IST

Like 0 people liked this

this is a question of my brothers 8th class holiday home work.plz tell the answer with a proper soln no matter how tough it is i'll explain it to him.

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

23 Jun 2009 14:51:41 IST

Like 0 people liked this

NugoRama

Blazing goIITian

Joined: 11 Mar 2009

Posts: 5564

23 Jun 2009 14:59:02 IST

Like 0 people liked this

1 month and 12 days ...No solution yet.

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

23 Jun 2009 15:04:44 IST

Like 0 people liked this

no re

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

23 Jun 2009 15:05:08 IST

Like 0 people liked this

m still stuck with this

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

23 Jun 2009 17:22:48 IST

Like 0 people liked this

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

23 Jun 2009 20:15:10 IST

Like 0 people liked this

........... plz sum 1 reply

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

Posts: 2717

23 Jun 2009 21:57:06 IST

Like 0 people liked this

i am able to get 8 solutions lol :D trying to find a way ...

ghfh bgd

Cool goIITian

Joined: 21 Apr 2009

Posts: 70

24 Jun 2009 22:26:41 IST

Like 0 people liked this

I guess there are infinite solutions

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

25 Jun 2009 14:21:51 IST

Like 0 people liked this

ya i also think there r infinite solns but it was mentioned that v would be surprised to no at just how many olns exist.

swapnil joshi

Blazing goIITian

Joined: 10 Apr 2009

Posts: 468

26 Jun 2009 09:25:54 IST

Like 0 people liked this

There are infinite solutions to this question . will come up with a proof in some days

swapnil joshi

Blazing goIITian

Joined: 10 Apr 2009

Posts: 468

26 Jun 2009 09:26:12 IST

Like 0 people liked this

Soumik

Blazing goIITian

Joined: 31 Jul 2008

Posts: 1266

26 Jun 2009 13:51:12 IST

Like 0 people liked this

$x_1^2+y_1^2+z_1^2<x^2+y^2+z^2\ (x_i , y_i, z_i)<(x_{i+1} , y_{i+1}, z_{i+1})$ ....................(1) x>x₁ y>y₁ z>z₁

Now observe

3xyzle x^2+y^2+z^2le xy+yz+zx

For proving this use the fact

x^2+y^2+z^2 >(x-y)^2+(y-z)^2+(z-x)^2 together with (x,y,z) ge 2 ...(Try it, I shall give it if u can't).

This proved suffices the case for x=y=z=1, by virtue of (1) above...

Thus no solutions exist!

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

Posts: 2717

26 Jun 2009 13:54:44 IST

Like 0 people liked this

So you are trying to say there exists no x,y,z satisfying the equation ?!?!?!?!

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

26 Jun 2009 19:46:04 IST

Like 0 people liked this

soumik see if we put x=y=z=1/15 then it is a soln of the given q but according to u no soln exists.hw would u explain this?

swapnil joshi

Blazing goIITian

Joined: 10 Apr 2009

Posts: 468

27 Jun 2009 10:04:46 IST

Like 0 people liked this

but dude you have taken x= y=z when given that

x<y<z?

Abhinav Jain

Blazing goIITian

Joined: 28 Apr 2009

Posts: 997

27 Jun 2009 19:03:52 IST

Like 0 people liked this

ohk i forgt the condition

Soumik

Blazing goIITian

Joined: 31 Jul 2008

Posts: 1266

28 Jun 2009 23:00:53 IST

Like 0 people liked this

@ Abhinav, according to the qsn, x,y,z are naturals, since when did 1/15 become a natural no.....?

Rudra, go ahead with ur solution.....

®µD®A

Blazing goIITian

Joined: 12 Apr 2008

Posts: 2717

29 Jun 2009 09:18:35 IST

Like 0 people liked this

the question asks for x,y,z to be natural but not 1/x,1/y,1/z ..

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