S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Tue, 2 Sep 2014 17:40:00 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: Range of abc
PostPosted: Fri, 18 May 2012 16:52:30 UTC 
Offline
Member

Joined: Sun, 8 Apr 2012 09:36:59 UTC
Posts: 29
suppose a,b,c are real numbers so that a+b+c = 15 and ab=ac=bc = 27.

Find the range of values that may obtained by the expression abc

My Process::

Let a,b,c be the roots of the cubic equation , Then formed cubic equation is

f(x) = x^3-(a+b+c).x^2+(ab+bc+ca).x-(abc)

So From given data

a+b+c = 15 and (ab+bc+ca) = 45

so f(x) = x^3-15x^2+45x-(abc)

Now Help Required..


Top
 Profile  
 
 Post subject: Re: Range of abc
PostPosted: Fri, 18 May 2012 17:13:20 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6844
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
jacks wrote:
suppose a,b,c are real numbers so that a+b+c = 15 and ab=ac=bc = 27.

Find the range of values that may obtained by the expression abc

My Process::

Let a,b,c be the roots of the cubic equation , Then formed cubic equation is

f(x) = x^3-(a+b+c).x^2+(ab+bc+ca).x-(abc)

So From given data

a+b+c = 15 and (ab+bc+ca) = 45

so f(x) = x^3-15x^2+45x-(abc)

Now Help Required..


I think you made a typo. ab=ac=bc\neq 0 would mean a=b=c. Also, where does the 45 come from?

What do you know about the graph of f(x)?

_________________
\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  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

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