Respuesta :

LammettHash

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]