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2 solutions
Going by this logic x = root to the power 5 of 1,which is 1. In that case the first equation is false, since 1 power 4 + 1 power 3.... Is equal to 5 and not 0. The answer is - 1, because only then the first equation is true
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Wrong. x 5 = 1 ⟹ x = 1 is false. Instead, x = e 5 2 π ι k , k = { 0 , … , 4 } . In this case, k = 0 , but x 5 = 1
You could have subtracted the two equations to eliminate a step. Pretty much the same thing but 1 step shorter.
x^4+x^3+x^2+x+1=0
multiply x on both sides
x^5+x^4+x^3+x^2+x
from question we get x^4+x^3+x^2+x+1=0
x^4+x^3+x^2+x=-1 substitute it in above equation
x^5-1=0
x^5=1
x 4 + x 3 + x 2 + x + 1 = 0
Multiplying by x
x 5 + x 4 + x 3 + x 2 + x = 0
From question, its obvious that
x 4 + x 3 + x 2 + x = − 1
So x 5 − 1 = 0
x 5 = 1