cube roots of unity..

Algebra Level 2

find the value of following equation

1 can't be determined 0 -3 5

Gaurav Yadav by Gaurav Yadav , 23, India

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2 solutions

Otto Bretscher
Mar 30, 2015

x 4 − x = x ( x 3 − 1 ) = x ( x − 1 ) ( x 2 + x + 1 ) = 0 x^4-x=x(x^3-1)=x(x-1)(x^2+x+1)=0

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Daksh Shami
Mar 26, 2015

From the given equation, we can deduce that x^2 = -x -1
so x^4 = (x+1)^2
Putting this in the problem x^4 - x , we get
x^2 + 1 + 2x - x
x^2 + x + 1
As this is equivalent to the given equation, hence the answer is 0


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