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Olympiad Question:

  1. Sep 14, 2008 #1
    If [tex]\alpha,\beta\ and\ \gamma[/tex] are the roots of the eqn.

    (x-a)(x-b)(x-c)+1=0

    then show that [tex](\alpha-x)(\beta-x)(\gamma-x)+1=0[/tex]
     
  2. jcsd
  3. Sep 14, 2008 #2
    Do you mean we should show that [tex](\alpha-x)(\beta-x)(\gamma-x)+1=0[/tex] for all x? What about [tex]x=\alpha[/tex], isn't that a counterexample? Maybe I'm missing something vital, but to me it seems incorrect.
     
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