Question

. If alpha, beta are the roots of the equation x2 + x + 1 = 0, find the value of alpha cube + beta cube​

Answer 1

Answer:

x

2

−x+1=0

⇒x=

2

1±

3

i

=−ω,−ω

2

, where ω,ω

2

are the cube roots of unity

⇒α=−ω,β=−ω

2

So α

2015

=(−ω)

2015

=−(ω)

2013+2

=−(ω)

671×3

⋅ω

2

=−ω

2

and β

2015

=(−ω

2

)

2015

=−(ω)

4030

=−(ω)

4029+1

=−(ω)

1343×3

⋅ω=−ω

Clearly the roots are same, that of given quadratic equation

Hence the quadratic equation will be same, which is x

2

−x+1=0

Explanation:

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