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