Question
2.2 .3 \quad 3 x^{\frac{2}{3}}-7 x^{\frac{1}{5}}+2=0
Ask by Gibson Reese. in South Africa
Feb 21,2025
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Answer
The equation \(3x^{\frac{2}{3}}-7x^{\frac{1}{5}}+2=0\) cannot be solved using the available methods.
Solution
The equation \(3x^{\frac{2}{3}}-7x^{\frac{1}{5}}+2=0\) cannot be solved using the available methods. If you need help solving this equation, please provide more context or information about the equation.
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Simplify this solution Bonus Knowledge
To tackle the equation \(3 x^{\frac{2}{3}} - 7 x^{\frac{1}{5}} + 2 = 0\), you might find it helpful to use substitution. Let’s define \(y = x^{\frac{1}{15}}\). Then \(x^{\frac{2}{3}} = y^{10}\) and \(x^{\frac{1}{5}} = y^3\). This transforms the equation into a polynomial form, making it easier to solve for \(y\). Once you obtain the values of \(y\), it's a fun process of reverting back to find the original variable \(x\) via \(x = y^{15}\). Keep an eye out for extraneous roots introduced during the substitution, as they can lead to confusion when validating your solutions.
