Question

if alpha and beta are cubes roots of unity alpha4+ beta4+1 upon alpha beta​

Answer 1

Answer:

$\alpha = \: w \:, \beta = w^{2} \\ = \alpha^{4} + \beta^{4} + \frac{1}{ \alpha } + \frac{1}{ \beta } \\ = \alpha^{4} + \beta^{4} + \frac{ \alpha + \beta }{ \alpha \beta } \\ = therefore \: ,w^{4} + (w^{2})^{4} + \frac{w + w^{2} }{ww^{2} } \\ = w + w^{8} + \frac{ - 1}{w^{3} } \\ = w + w^{2} + \frac{ - 1}{1} \\ = - 1 - 1 \\ Ans: = - 2$

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