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27-12-2023
Mathematics

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If [tex]p+qi[/tex] is a root of [tex]x^{3}-x-6=0[/tex], where [tex]p[/tex] and [tex]q[/tex] are real:
a. Prove that [tex]-6-p+p^3 -3pq^2=0[/tex] and [tex]1-3p^2+q^2=0[/tex]
b. Hence, prove that [tex]p-qi[/tex]also is a root

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