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What the value of n ?

  1. Feb 13, 2007 #1
    hi guys ... i am new here ... could you please help me in this ?

    X ^ 3 + ( x + 2 ) ^ n + ( 2 - x ) ^ n = 0
    whats the value of n ?! :bugeye:
     
  2. jcsd
  3. Feb 13, 2007 #2
    Your question is ill defined. If you mean "What value of n satisfies this FOR ALL X?" then there isn't one. You can see this by working out the coefficent of [tex]x^{3}[/tex] in [tex](x+2)^{n}+(2-x)^{n}[/tex] and working out what value of n gives that coefficent as -1, so that it cancels with the [tex]x^{3}[/tex] term. Unfortunately, this leaves you with other terms which don't cancel (linear ones).

    For any value of n you're going to find a value of x which satisfies the equation, though it will depend on n.

    So basically no n gives it true for all x but any value of n makes it true for some x.
     
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