Rheasingh11 Rheasingh11

20-01-2020
Mathematics

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5. If x + x-1 = a, express x2 + 2 + x-2 in terms of a.

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LammettHash LammettHash

20-01-2020

I suppose the question is, if [tex]x+x^{-1}=a[/tex], what is [tex]x^2+2+x^{-2}[/tex]?

Recall that [tex](a+b)^2=a^2+2ab+b^2[/tex]. It follows that for [tex]x\neq0[/tex],

[tex]x^2+2+x^{-2}=x^2+2xx^{-1}+(x^{-1})^2=(x+x^{-1})^2=\boxed{a^2}[/tex]

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