Question Number 83554 by Power last updated on 03/Mar/20
Answered by MJS last updated on 03/Mar/20
$${x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} −\mathrm{8}{x}+\frac{\mathrm{17}}{\mathrm{5}}=\mathrm{0} \\ $$$$\mathrm{let}\:{x}={t}−\mathrm{1} \\ $$$${t}^{\mathrm{4}} −\mathrm{6}{t}^{\mathrm{2}} +\frac{\mathrm{42}}{\mathrm{5}}=\mathrm{0} \\ $$$${t}^{\mathrm{2}} =\mathrm{3}\pm\frac{\sqrt{\mathrm{15}}}{\mathrm{5}} \\ $$$${t}=\pm\sqrt{\mathrm{3}\pm\frac{\sqrt{\mathrm{15}}}{\mathrm{5}}} \\ $$$${x}=−\mathrm{1}\pm\sqrt{\mathrm{3}\pm\frac{\sqrt{\mathrm{15}}}{\mathrm{5}}} \\ $$