Final answer to the problem
$y=\frac{\sqrt[3]{-3x^2+\sqrt[4]{2}}}{\sqrt[3]{2}},\:y=\left(\frac{-\left(3x^2+\sqrt[4]{2}\right)}{2}\right)^{\frac{1}{3}}$
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Step-by-step Solution
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1
Removing the variable's exponent
$\sqrt[4]{\left(3x^2+2y^3\right)^4}=\pm \sqrt[4]{2}$
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$\sqrt[4]{\left(3x^2+2y^3\right)^4}=\pm \sqrt[4]{2}$
Learn how to solve problems step by step online. Solve the equation (3x^2+2y^3)^4=2. Removing the variable's exponent. Cancel exponents 4 and \frac{1}{4}. We need to isolate the dependent variable , we can do that by simultaneously subtracting 3x^2 from both sides of the equation. As in the equation we have the sign \pm, this produces two identical equations that differ in the sign of the term \sqrt[4]{2}. We write and solve both equations, one taking the positive sign, and the other taking the negative sign.
Final answer to the problem
$y=\frac{\sqrt[3]{-3x^2+\sqrt[4]{2}}}{\sqrt[3]{2}},\:y=\left(\frac{-\left(3x^2+\sqrt[4]{2}\right)}{2}\right)^{\frac{1}{3}}$