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a-8-a-4-1-a-4-a-2-1-




Question Number 57245 by ANTARES VY last updated on 01/Apr/19
((a^8 +a^4 +1)/(a^4 +a^2 +1))=?
$$\frac{\boldsymbol{\mathrm{a}}^{\mathrm{8}} +\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\mathrm{1}}=? \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19
a^8 +a^4 +1  a^8 +2a^4 +1−a^4   (a^4 +1)^2 −(a^2 )^2   (a^4 +a^2 +1)(a^4 −a^2 +1)  so ans is  a^4 −a^2 +1
$${a}^{\mathrm{8}} +{a}^{\mathrm{4}} +\mathrm{1} \\ $$$${a}^{\mathrm{8}} +\mathrm{2}{a}^{\mathrm{4}} +\mathrm{1}−{a}^{\mathrm{4}} \\ $$$$\left({a}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} −\left({a}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$$$\left({a}^{\mathrm{4}} +{a}^{\mathrm{2}} +\mathrm{1}\right)\left({a}^{\mathrm{4}} −{a}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$${so}\:{ans}\:{is} \\ $$$${a}^{\mathrm{4}} −{a}^{\mathrm{2}} +\mathrm{1} \\ $$

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