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If-0-lt-c-2-lt-4-27-and-m-4c-2-m-1-m-2-m-1-m-2-3c-2-2-then-find-real-values-of-m-in-terms-of-c-2-




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

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