Question Number 61140 by MJS last updated on 29/May/19
$$\mathrm{can}\:\mathrm{we}\:\mathrm{find}\:\mathrm{an}\:\mathrm{exact}\:\mathrm{solution}? \\ $$$${t}^{\mathrm{6}} +\mathrm{4}{t}^{\mathrm{4}} −\mathrm{12}{t}^{\mathrm{3}} +\mathrm{24}{t}^{\mathrm{2}} −\mathrm{24}{t}+\mathrm{8}=\mathrm{0} \\ $$
Commented by ajfour last updated on 04/Jun/19
$${whats}\:{the}\:{source}\:{of}\:{this}\:{question}, \\ $$$${Is}\:{there}\:{a}\:{way}\:{to}\:{solve}\:{it},\:{afterall} \\ $$$${Sir}? \\ $$
Answered by ajfour last updated on 30/May/19
$$\left\{{t}^{\mathrm{2}} \left({t}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} +\mathrm{20}{t}^{\mathrm{2}} +\mathrm{8}\right\}^{\mathrm{2}} =\mathrm{144}{t}^{\mathrm{2}} \left({t}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} \\ $$$${let}\:{t}^{\mathrm{2}} ={s} \\ $$$$\Rightarrow\:\left\{{s}\left({s}+\mathrm{2}\right)^{\mathrm{2}} +\mathrm{20}{s}+\mathrm{8}\right\}^{\mathrm{2}} =\mathrm{144}{s}\left({s}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$…… \\ $$