What the value of n ?

[RauLiTo]

Main Question or Discussion Point

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 ?!

 

[AlphaNumeric]

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 $$x^{3}$$ in $$(x+2)^{n}+(2-x)^{n}$$ and working out what value of n gives that coefficent as -1, so that it cancels with the $$x^{3}$$ 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.