Question

solve the equation (x-1)power 3+8=0​

Answer 1

−1,1−2ω,1−2

Step-by-step explanation:

I’m assuming that you are aware about cube roots of unity. This question asks us to find the roots in terms of ω.ω. So, rewrite the equation as:

(x−1)3=−8(x−1)3=−8

=>(x−1)3=(−2)3(x−1)3=(−2)3

=> (x−1−2)3=1(x−1−2)3=1

Let t=x−1−2.t=x−1−2. So, t3=1=>t=1,ωt3=1=>t=1,ω or ω2ω2

t=1:t=1:

t=x−1−2=1=>x=−1t=x−1−2=1=>x=−1

t=ω:t=ω:

t=x−1−2=ω=>x=1−2ωt=x−1−2=ω=>x=1−2ω

t=ω2:t=ω2:

t=x−1−2=ω2=>x=1−2ω2t=x−1−2=ω2=>x=1−2ω2

So, the roots are −1,1−2ω,1−2