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 June 6th, 2012, 06:12 PM #1 Member   Joined: May 2012 Posts: 86 Thanks: 0 Equation... Find all groups of three real numbers (x,y,z), such that (x-1)/y = (y-1)/z = (z-1)/x June 6th, 2012, 11:35 PM #2 Member   Joined: May 2012 From: Chennai,India Posts: 67 Thanks: 0 Re: Equation... June 7th, 2012, 02:38 PM   #3
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Re: Equation...

Quote:
 Originally Posted by karthikeyan.jp
Your solution is simply x = y = z ? 0.

Are there solutions where they are not all equal. June 7th, 2012, 02:48 PM   #4
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Re: Equation...

Quote:
Originally Posted by mathman
Quote:
 Originally Posted by karthikeyan.jp
Your solution is simply x = y = z ? 0.

Are there solutions where they are not all equal.
Since it is symmetric on x,y,z, without loss of generality let x<=y<=z.
If we assume x<y<=z or x<=y<z or x<y<z; then which is impossible since both are equal to m.
The only remaining alternative is x=y=z, which obviously holds. Tags equation 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 PhizKid Differential Equations 0 February 24th, 2013 10:30 AM mich89 Algebra 3 January 9th, 2013 01:22 PM xujack88 Calculus 8 December 11th, 2009 07:04 PM

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