If $$x^4+x^3+x^2+x+1 = 0$$, then the value of $$x^{25}$$ is __FILLWRAPs__

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Uniteasy Admin · Accepted Answer

Given
$$x^4+x^3+x^2+x+1 = 0$$n
Multiply both sides with $$x$$ to raise the power of leading term to $$5$$
$$x^5+x^4+x^3+x^2+x= 0$$n
Subtracting (1) from (2) gives
$$x^5-1 = 0$$c
Then
$$x^5 = 1$$c
Using power rule for exponent
$$x^{25} = (x^5)^5 = 1^5 = 1$$
Therefore
the value of $$x^{25}$$ is $$1$$

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