Show that \sqrt{-1-\sqrt{-1-{\sqrt{-1...}}}} can be expressed in the form \alpha\

Averie Ray

Averie Ray

Answered question

2022-04-25

Show that 11{1} can be expressed in the form α or α2, Hence prove
(a+bα+cα2)(a+bα2+cα)=12(ab)2+(bc)2+(ca)2

Answer & Explanation

louran20z47

louran20z47

Beginner2022-04-26Added 14 answers

The LHS is a2+b2α3+c2α3+ab(α2+α)+ac(α2+α)+bc(α4+α)
Use the fact that α4=α
So The LHS becomes
a2+b2+c2abacbc

=12[a2+b22ab+b2+c22bc+a2+c22ac]

=12[(ab)2+(bc)2+(ac)2]

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