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Question Number 184828 by ajfour last updated on 12/Jan/23

Find x in terms of   c  ∀ 0<c<(2/(3(√3)))  (3x^2 −1)(3x^2 +36x−1)^2            ={4(x^3 −x−c)+9(7x^2 +1)}^2

$${Find}\:{x}\:{in}\:{terms}\:{of}\:\:\:{c}\:\:\forall\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$ $$\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{36}{x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$ $$\:\:\:\:\:\:\:\:\:=\left\{\mathrm{4}\left({x}^{\mathrm{3}} −{x}−{c}\right)+\mathrm{9}\left(\mathrm{7}{x}^{\mathrm{2}} +\mathrm{1}\right)\right\}^{\mathrm{2}} \\ $$

Commented byFrix last updated on 12/Jan/23

Not possible at all.

$$\mathrm{Not}\:\mathrm{possible}\:\mathrm{at}\:\mathrm{all}. \\ $$

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