Grade 12Algebra
w is the cubic root of unity then root w+ root w^2=?
w is the cubic root of unity then root w+ root w^2=?
2 Answers
Aditya Gupta
Approved Tutor Answer6 Years agow^3=1
w^3 – 1= 0
(w – 1)(w^2+w+1)= 0
assuming w is not 1 itself
w^2+w+1= 0
or w^2+w= – 1
now, let x= root w+ root w^2
x^2 = w + w^2 + 2root(w^3)
= – 1 + 2root(1)
= 1
so x= ± 1
kindly approve :))
Arun
Dear student
w^3 = 1
w^3 – 1 = 0
(w – 1) (w^2 + 1 + w) = 0
hence w + w^2 = -1 only
Hope it helps
Regards
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