The value of :
(a+bw+cw​2)/(b+cw+aw​2) +(a+bw+cw​2)/(c+aw+w​2) is,
1). 1
2). -1
3). 2
4). -2

where, w represents omega.

Dear Student,
Please find below the solution to the asked query:

We know that 1,ω and ω2 are roots of the equation x3-1=0 and are known as cube roots of unity.Now, we know that ,1+ω+ ω2=0ω3=1 ω3n=1 , where 'n' is any integer.  ω4=ω3.ωω4=ωThere is a printing error in your question. In the denominator of second term it should be 2 rather than ω2.Let S=a+bω+cω2b+cω+aω2+a+bω+cω2c+aω+bω2 S=ωωa+bω+cω2b+cω+aω2+ω2ω2a+bω+cω2c+aω+bω2 S=ωa+bω+cω2bω+cω2+aω3+ω2a+bω+cω2cω2+aω3+bω4Now putting ω3=1 and ω4=ω , we get, S=ωa+bω+cω2bω+cω2+a+ω2a+bω+cω2cω2+a+bω S=ωa+bω+cω2a+bω+cω2+ω2a+bω+cω2a+bω+cω2 S=ω+ω2Now 1+ω+ω2=0ω+ω2=-1S=-1Hence option2 is correct.

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