Final answer to the problem
$y=\frac{\sqrt[3]{2x^2-9}-1}{x}$
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Step-by-step Solution
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1
Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{3}$
$\left(\left(1+xy\right)^3\right)^{\frac{1}{3}}=\left(2x^2-9\right)^{\frac{1}{3}}$
Learn how to solve quotient rule of differentiation problems step by step online.
$\left(\left(1+xy\right)^3\right)^{\frac{1}{3}}=\left(2x^2-9\right)^{\frac{1}{3}}$
Learn how to solve quotient rule of differentiation problems step by step online. Solve the equation (1+xy)^3=2x^2-9. Removing the variable's exponent raising both sides of the equation to the power of \frac{1}{3}. Divide 1 by 3. Simplify \sqrt[3]{\left(1+xy\right)^3} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{3}. Multiply 3 times \frac{1}{3}.
Final answer to the problem
$y=\frac{\sqrt[3]{2x^2-9}-1}{x}$