My Math Forum Equation system

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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
 September 7th, 2017, 10:29 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,168 Thanks: 1640 If you try letting a = b = c, you get a³ - 2a² - a + 2 = 0, i.e. (a + 1)(a - 1)(a - 2) = 0.
 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?
 September 7th, 2017, 01:15 PM #4 Global Moderator   Joined: May 2007 Posts: 6,540 Thanks: 591 Skipjack doesn't need to prove anything. He has demonstrated that there is a particular solution when a=b=c.
 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"
 September 8th, 2017, 04:09 AM #6 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,237 Thanks: 884 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?
September 8th, 2017, 05:42 AM   #7
Math Team

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Quote:
 Originally Posted by Zuben ....the profesor give me 0 points and write "how you know it, and why you think that there arent more solution"
we can confirm it's ok to give you the solution?
Thank you.

 September 8th, 2017, 06:00 AM #8 Global Moderator   Joined: Dec 2006 Posts: 19,168 Thanks: 1640 Hint: rearrange each equation.
 September 8th, 2017, 08:00 PM #9 Global Moderator   Joined: Dec 2006 Posts: 19,168 Thanks: 1640 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).

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