Question Number 158383 by HongKing last updated on 03/Nov/21
$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tan}^{\mathrm{4}} \left(\boldsymbol{\mathrm{x}}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{10}}\:=\:\frac{\mathrm{2}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)} \\ $$$$ \\ $$
Answered by MJS_new last updated on 03/Nov/21
$$\mathrm{easy}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{10}}=\frac{\mathrm{2}}{\mathrm{1}+\mathrm{3}{t}^{\mathrm{2}} } \\ $$$${t}^{\mathrm{6}} −\frac{\mathrm{19}}{\mathrm{3}}{t}^{\mathrm{4}} +\mathrm{11}{t}^{\mathrm{2}} −\mathrm{3}=\mathrm{0} \\ $$$$\left({t}^{\mathrm{2}} −\mathrm{3}\right)^{\mathrm{2}} \left({t}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}}\right)=\mathrm{0} \\ $$$$\mathrm{now}\:\mathrm{finish}\:\mathrm{it} \\ $$
Commented by HongKing last updated on 04/Nov/21
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\boldsymbol{\mathrm{S}}\mathrm{er}\:\mathrm{cool} \\ $$