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Enter all positive solutions to $4x^{1/3}-2\frac{x}{x^{2/3}}=7+\sqrt[3]{x}/2$.

 Apr 28, 2022
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\( $4x^{1/3}-2\frac{x}{x^{2/3}}=7+\sqrt[3]{x}/2$\)

 

4x^(1/3) - 2x^(1/3)  =  7  + x^(1/3)  / 2

 

2x^(1/3)  = 7  + x^(1/3) / 2           multiply through by 2

 

4x^(1/3)  = 14  + x^(1/3)

 

3x^(1/3)  =  14

 

x^(1/3)  = 14 / 3                  cube both sides

 

x = (14/ 3)^3  =  2744 /  27

 

 

cool cool cool

 Apr 28, 2022

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