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Question-155023




Question Number 155023 by ajfour last updated on 24/Sep/21
Commented by ajfour last updated on 24/Sep/21
The blue area is equal to the  brown area. Find x in terms  of c.
$${The}\:{blue}\:{area}\:{is}\:{equal}\:{to}\:{the} \\ $$$${brown}\:{area}.\:{Find}\:{x}\:{in}\:{terms} \\ $$$${of}\:{c}. \\ $$
Commented by benjo_mathlover last updated on 25/Sep/21
⇔ x = ((((√3) (√(2+c^2 +4)) +9c))^(1/3) /( ((18))^(1/3) )) − ((2)^(1/3) /( ((3(√3) (√(27c^2 +4)) +27c))^(1/3) ))
$$\Leftrightarrow\:\mathrm{x}\:=\:\frac{\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{3}}\:\sqrt{\mathrm{2}+\mathrm{c}^{\mathrm{2}} +\mathrm{4}}\:+\mathrm{9c}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{18}}}\:−\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{3}\sqrt{\mathrm{3}}\:\sqrt{\mathrm{27c}^{\mathrm{2}} +\mathrm{4}}\:+\mathrm{27c}}}\: \\ $$
Answered by mahdipoor last updated on 24/Sep/21
x^3 +x=c
$${x}^{\mathrm{3}} +{x}={c} \\ $$

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