S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Fri, 24 May 2013 10:32:00 UTC

View unanswered posts | View active topics


Board index » High School and College Mathematics » Algebra

All times are UTC [ DST ]



Post new topic Reply to topic  Page 1 of 1
  [ 10 posts ] 
  Print view Previous topic | Next topic 
Author Message
kreshnik
 Post subject: I need help badly !
PostPosted: Sun, 25 Dec 2011 12:21:11 UTC 
Offline
Senior Member
User avatar

Joined: Sun, 25 Dec 2011 00:28:25 UTC
Posts: 95
what should I do with these??!

1. x^3-y^3=28 and x-y=4, then ... x^2+xy+y^2=?




2. x+y=9 , x*y=8 then ... x^3+y^3=?


sorry for interrupting..
Top
 Profile  
 
Denis
 Post subject: Re: Linear Equations
PostPosted: Sun, 25 Dec 2011 12:29:32 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
Please start your own thread...see "newtopic" button?

_________________
I'm not prejudiced...I hate everybody equally!
Top
 Profile  
 
outermeasure
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 12:54:42 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6008
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Topic split.

_________________
\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
Top
 Profile  
 
outermeasure
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 12:55:57 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6008
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
kreshnik wrote:
what should I do with these??!

1. x^3-y^3=28 and x-y=4, then ... x^2+xy+y^2=?




2. x+y=9 , x*y=8 then ... x^3+y^3=?


sorry for interrupting..


What have you tried?

_________________
\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
Top
 Profile  
 
Denis
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 18:24:27 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
kreshnik wrote:
2. x+y=9 , x*y=8 then ... x^3+y^3=?

Your English is quite good; better than some around here!!
You got that one right. Good work.

May have been easier this way:
x + y = 9 ; y = 9 - x [1]
xy = 8 [2]
Substitute [1] in [2]:
x(9 - x) = 8
9x - x^2 = 8
x^2 - 9x + 8 = 0 ; factor:
(x - 8)(x - 1) = 0
x = 8 or x = 1
Substitute in [1]:
y = 9-8 = 1 or y = 9-1 = 8

x^3 + y^3 = 8^3 + 1^3 = 513
or
x^3 + y^3 = 1^3 + 8^3 = 513

That's just another way of doing it...

_________________
I'm not prejudiced...I hate everybody equally!
Top
 Profile  
 
Denis
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 18:35:05 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
kreshnik wrote:
1. x^3-y^3=28 and x-y=4, then ... x^2+xy+y^2=?

You were ok up to this line:
-3yxx + 3yyx = 64 - 28 ; then you somehow got your signs wrong; should be:

3xy^2 - 3yx^2 = 36 ; divide by 3:
xy^2 - yx^2 = 12

Substitute x = y + 4 (from the given x - y = 4):
y^2(y + 4) - y(y + 4)^2 = 12

I'll let you finish it...

_________________
I'm not prejudiced...I hate everybody equally!
Top
 Profile  
 
kreshnik
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 18:55:45 UTC 
Offline
Senior Member
User avatar

Joined: Sun, 25 Dec 2011 00:28:25 UTC
Posts: 95
Thanks a lot my friend...I appreciate that.
Thanks again :)
Top
 Profile  
 
Denis
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 19:03:08 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
kreshnik wrote:
Thanks a lot my friend...

THANK YOU: I had no friends before :oops:

_________________
I'm not prejudiced...I hate everybody equally!
Top
 Profile  
 
mathematic
 Post subject: Re: I need help badly !
PostPosted: Sun, 25 Dec 2011 23:05:42 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Fri, 1 Jul 2011 01:17:26 UTC
Posts: 322
kreshnik wrote:
what should I do with these??!

1. x^3-y^3=28 and x-y=4, then ... x^2+xy+y^2=?




2. x+y=9 , x*y=8 then ... x^3+y^3=?


sorry for interrupting..

1. is very easy when you recognize x^3 - y^3 = (x - y)(x^2 + xy +y^2)

2. is slightly harder: (x + y)^3 = x^3 + 3yx^2 + 3xy^2 + y^3 = x^3 + y^3 + 3(x + y)xy.
Top
 Profile  
 
Shadow
 Post subject: Re: I need help badly !
PostPosted: Mon, 26 Dec 2011 00:38:16 UTC 
Offline
Moderator
User avatar

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
mathematic wrote:
kreshnik wrote:
what should I do with these??!

1. x^3-y^3=28 and x-y=4, then ... x^2+xy+y^2=?




2. x+y=9 , x*y=8 then ... x^3+y^3=?


sorry for interrupting..

1. is very easy when you recognize x^3 - y^3 = (x - y)(x^2 + xy +y^2)

2. is slightly harder: (x + y)^3 = x^3 + 3yx^2 + 3xy^2 + y^3 = x^3 + y^3 + 3(x + y)xy.


They have the first one first for a reason, you realize how to get x^2+y^2 from xy and (x+y)^2, then you can easily do the second one using x^3+y^3=(x+y)(x^2-xy+y^2).

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 10 posts ] 

Board index » High School and College Mathematics » Algebra

All times are UTC [ DST ]

Who is online

Users browsing this forum: No registered users

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA