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 September 18th, 2009, 11:41 AM #1 Senior Member   Joined: Apr 2009 Posts: 201 Thanks: 0 is this a valid proof? Hello, I was hoping that you guyscould check my work: show that (x+y)^3 = x^3 + y^3 only if x = 0, y = 0 or x = -y. So, x^3 + 3x^2y + 3xy^2 + y^3 = x^3 + y^3 --> 3xy^2 + 3x^2y = 0. The first case is trivial, if x and y are both zero then the equation equals to zero (I'm not sure if I should prove that, it seems a bit tedious) then, if x does not equal to zero, 3xy^2 = - 3x^2y --> 3y^2 x * x^-1 = -3x^2 * x^-1 y --> 3y^2 = - 3yx (by inverses and commutativity) So, if a * b = a * c = 0, either a is zero or b =c - if 3y*y = -3y*x then either 3y = 0 or y = -x. If 3y = 0 then y = 0 If y does not equal to zero, repeat the same method revolving 3x and x = -y 3xy^2 = - 3x^2y --> 3y^2x * y^-1 = -3x^2 y * y^-1 --> 3x^2 = - 3yx So, if a * b = a * c = 0, either a is zero or b =c - if 3y*y = -3y*x then either 3x = 0 or x = -y. If 3x = 0 then x = 0. I'm not sure what I should include in my proofs, some things just seem to be so tedious and unnecessary (like proving that -(ab) = (-a)(b) or (a)(-b) every time, or a*0 = 0). thanks September 18th, 2009, 11:50 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 It's a bit longwinded - if you correctly surmise that but just factorising this and dividing by 3 gives you What does this tell you? September 18th, 2009, 11:57 AM   #3
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 Originally Posted by mattpi It's a bit longwinded - if you correctly surmise that but just factorising this and dividing by 3 gives you What does this tell you?
right.. I need to pay more attention, thanks September 19th, 2009, 01:12 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,935 Thanks: 2209 The answer follows immediately without having to divide by three first. September 19th, 2009, 05:05 AM #5 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Well, of course... it's just neater without the 3  Tags proof, valid Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post eddybob123 Number Theory 2 August 1st, 2013 09:21 PM zeraoulia Complex Analysis 2 January 28th, 2013 02:37 AM rummi Real Analysis 1 November 21st, 2012 07:19 PM rummi Real Analysis 1 October 5th, 2012 12:11 PM rummi Calculus 3 September 26th, 2012 02:54 PM

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