## Answers

### This Is a Certified Answer

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So given

x² + x + 1 = 0 ⇒ x² + x + 1 - 1 + 1 = 0 ⇒ x² + x - 1 = -2

so

so x(x² + x + 1) = x³ + x² + x + 1 - 1

x² + x + 1 = (x³ + 1)/x + (x² + x - 1)/x

0 = (x³ + 1)/x + (x² + x - 1)/x

- (x² + x - 1)/x = (x³ + 1)/x

- ( - 2) = (x³ + 1)

x³ + 1 = 2

so value for

x² + x + 1 = 0 ⇒ x² + x + 1 - 1 + 1 = 0 ⇒ x² + x - 1 = -2

so

so x(x² + x + 1) = x³ + x² + x + 1 - 1

x² + x + 1 = (x³ + 1)/x + (x² + x - 1)/x

0 = (x³ + 1)/x + (x² + x - 1)/x

- (x² + x - 1)/x = (x³ + 1)/x

- ( - 2) = (x³ + 1)

x³ + 1 = 2

so value for

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

as x^2+x+1=0 it is obvious that x is not equal to 1.

x^2+x+1=0

(x-1)(x^2+x+1)=0

x^3-1=0

x^3=1

so x is the cube root of unity,

x = 1, w, w^2... here w is omega

now x^3+1 = w^3 + 1 = 1 + 1 = 2

and 1/w = w^2

So, ( (x^3+1)/x )^3 = (2 w^2)^3 = 8 w^6 = 8 (w^3)^2 = 8

this is the correct way of solving...