Results 1 to 3 of 3

Math Help - solve system of equations

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    91

    solve system of equations

    Solve the system in real x,y,z:
     (a+b)^3=8c , (a+c)^3=8b , (b+c)^3=8a
    The solution is clearly (a,b,c)=(0,0,0),(1,1,1),(-1,-1,-1), but I need some trick to "arrive" at it... any ideas?\
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856

    Re: solve system of equations

    Quote Originally Posted by atreyyu View Post
    Solve the system in real x,y,z:
     (a+b)^3=8c , (a+c)^3=8b , (b+c)^3=8a
    The solution is clearly (a,b,c)=(0,0,0),(1,1,1),(-1,-1,-1), but I need some trick to "arrive" at it... any ideas?\
    No, you do not need "tricks", you need understanding. The first thing you should see is that these three equations are "symmetric"- if you interchange a, b, or c in any one, you get another one. That tells you that a= b= c. With b and c replaced by a, all three equations reduce to (a+ a)^3= 8a^3= 8a so that a^3= a and a^3- a= a(a^2- 1)= a(a-1)(a+1)= 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    91

    Re: solve system of equations

    Quote Originally Posted by HallsofIvy View Post
    That tells you that a= b= c.
    I was wondering if we were allowed to make that conjecture...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Please help solve these system of equations
    Posted in the Algebra Forum
    Replies: 10
    Last Post: January 8th 2011, 03:17 PM
  2. [SOLVED] Solve system of equations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 23rd 2010, 08:10 PM
  3. How to solve this system of equations?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 20th 2009, 11:41 AM
  4. Solve the System of equations
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 1st 2008, 08:41 AM
  5. Solve the system of equations
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 11th 2007, 10:12 AM

Search Tags


/mathhelpforum @mathhelpforum