Question

find the equation whose roots are a+b, aw²+bw, aw+bw² where w is the cube root of unity​

Answer 1

Answer:

Mark me as brilliant list

Step-by-step explanation:

Correct option is

B

3(a

3

+b

3

)

Taking

x=a+b

y=aω+bω

2

z=aω

2

+bω

We have

x+y+z=a(1+ω+ω

2

)+b(1+ω+ω

2

)=0 as 1+ω+ω

2

=0

So,

x

3

+y

3

+z

3

=3xyz

=3(a+b)(aω+bω

2

)(aω

2

+bω)

=3(a+b)(a

2

−ab+b

2

)

=3(a

3

+b

3

)