My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 7th, 2017, 10:01 AM   #1
Newbie
 
Joined: Sep 2017
From: London

Posts: 3
Thanks: 0

Equation system

Plis, I need help.
The order is: "Solve in real numbers"
a^2 * b + 2 = a + 2*b*c
b^2 * c + 2 = b + 2*a*c
c^2 * a + 2 = c + 2*a*b
Zuben is offline  
 
September 7th, 2017, 10:29 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 17,919
Thanks: 1385

If you try letting a = b = c, you get a³ - 2a² - a + 2 = 0, i.e. (a + 1)(a - 1)(a - 2) = 0.
skipjack is offline  
September 7th, 2017, 10:35 AM   #3
Newbie
 
Joined: Sep 2017
From: London

Posts: 3
Thanks: 0

Yeah but how to prove that a=b=c and there are no more roots?
Zuben is offline  
September 7th, 2017, 01:15 PM   #4
Global Moderator
 
Joined: May 2007

Posts: 6,306
Thanks: 525

Skipjack doesn't need to prove anything. He has demonstrated that there is a particular solution when a=b=c.
mathman is offline  
September 7th, 2017, 10:23 PM   #5
Newbie
 
Joined: Sep 2017
From: London

Posts: 3
Thanks: 0

Yeah, but I cannot write "If a=b=c there are this 3 solutions-1,1,2" the profesor give me 0 points and write "how you know it, and why you think that there arent more solution"
Zuben is offline  
September 8th, 2017, 04:09 AM   #6
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,649
Thanks: 681

Yes, so you need to work out whether there are other solutions before you turn it in. Did you notice that all three equations are the same except that "a", "b", and "c" are rearranged?
Country Boy is offline  
September 8th, 2017, 05:42 AM   #7
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 10,473
Thanks: 693

Quote:
Originally Posted by Zuben View Post
....the profesor give me 0 points and write "how you know it, and why you think that there arent more solution"
Can we get your "profesor"'s email address so
we can confirm it's ok to give you the solution?
Thank you.
Denis is offline  
September 8th, 2017, 06:00 AM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 17,919
Thanks: 1385

Hint: rearrange each equation.
skipjack is offline  
September 8th, 2017, 08:00 PM   #9
Global Moderator
 
Joined: Dec 2006

Posts: 17,919
Thanks: 1385

This type of problem occurs from time to time in mathematics competitions, some of which are open competitions where the candidates are asked not to obtain help from internet forums. I haven't found the above problem on any other website, but I think it would be best not to provide further help other than general advice until some weeks have elapsed or it can be shown that the problem isn't from a current competition (for example, by showing that it appears in a published book).
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
equation, system



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Equation system MathematicsGeek Algebra 1 August 25th, 2015 07:03 AM
system of equation goldgold Algebra 2 December 26th, 2014 12:52 PM
System of equation Jhenrique Algebra 5 March 27th, 2014 03:12 AM
:) :D System of equation Rekooo Algebra 1 December 3rd, 2010 12:55 AM
help pleeeeease (system) equation Sara so Algebra 4 September 5th, 2010 01:36 PM





Copyright © 2017 My Math Forum. All rights reserved.