Find the Value of n in X^3 + (x+2)^n + (2-x)^n = 0 - Help Wanted!

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The equation X^3 + (x + 2)^n + (2 - x)^n = 0 does not have a value of n that satisfies the equation for all x. Analyzing the coefficients, specifically the coefficient of x^3 in (x + 2)^n + (2 - x)^n, reveals that no single n can cancel the x^3 term completely. While any chosen value of n will yield solutions for specific x values, it fails to provide a universal solution across all x.

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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:
 
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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 coefficient of [tex]x^{3}[/tex] in [tex](x+2)^{n}+(2-x)^{n}[/tex] and working out what value of n gives that coefficient 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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