Question Number 139642 by ajfour last updated on 30/Apr/21
$${If}\:\:\mathrm{0}<{c}^{\mathrm{2}} <\frac{\mathrm{4}}{\mathrm{27}}\:\:,\:{and} \\ $$$${m}\left\{\mathrm{4}{c}^{\mathrm{2}} −{m}\left(\mathrm{1}+{m}\right)^{\mathrm{2}} \right\} \\ $$$$\:\:\:\:\:=\left\{{m}\left(\mathrm{1}+{m}\right)^{\mathrm{2}} −\mathrm{3}{c}^{\mathrm{2}} \right\}^{\mathrm{2}} \:\:{then} \\ $$$${find}\:{real}\:{values}\:{of}\:{m}\:{in}\:{terms} \\ $$$${of}\:{c}^{\mathrm{2}} . \\ $$