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Question Number 71925 by Henri Boucatchou last updated on 22/Oct/19

 Solve  (√(1 − x^2 )) = x^(4/3)

$$\:\boldsymbol{{Solve}}\:\:\sqrt{\mathrm{1}\:−\:\boldsymbol{{x}}^{\mathrm{2}} }\:=\:\boldsymbol{{x}}^{\mathrm{4}/\mathrm{3}} \\ $$

Answered by MJS last updated on 23/Oct/19

x=t^(3/2)   (√(1−t^3 ))=t^2   1−t^3 =t^4   t^4 +t^3 −1=0  no useful exact solution  t≈.819173  ⇒ x=±.741418

$${x}={t}^{\mathrm{3}/\mathrm{2}} \\ $$$$\sqrt{\mathrm{1}−{t}^{\mathrm{3}} }={t}^{\mathrm{2}} \\ $$$$\mathrm{1}−{t}^{\mathrm{3}} ={t}^{\mathrm{4}} \\ $$$${t}^{\mathrm{4}} +{t}^{\mathrm{3}} −\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{no}\:\mathrm{useful}\:\mathrm{exact}\:\mathrm{solution} \\ $$$${t}\approx.\mathrm{819173} \\ $$$$\Rightarrow\:{x}=\pm.\mathrm{741418} \\ $$

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