How do you find three cube roots of $1$ ?

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Answer 1 · 2017-06-26T07:42:56

Three cube roots of $1$ are

$1$ , $(-1-isqrt3)/2$ and $(-1+isqrt3)/2$

Let $x=root(3)1$ , then $x^3=1$ or

$x^3-1=0$

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

Hence either $x=1$

or $x^2+x+1=0$ and using quadratic formula

$x=(-1+-sqrt(1-4xx1xx1))/2$

= $(-1+-sqrt(-3))/2$

= $(-1+-isqrt3)/2$

Hence three cube roots of $1$ are

$1$ , $(-1-isqrt3)/2$ and $(-1+isqrt3)/2$

How do you find three cube roots of 11?