Question 1004807
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{{{x^(2/3)}}} + {{{2}}} = {{{3x^(1/3)}}}.


Introduce new variable y = {{{root(3,x)}}}. Then your equation takes the form


{{{y^2}}} + {{{2}}} = {{{3y}}}, or


{{{y^2}}} - {{{3y}}} + {{{2}}} = {{{0}}}.


Solve this quadratic equation. You can use the quadratic formula, or the Viete's theorem, or factoring.


The roots are y = 1 and y = 2.


y = 1 -----> x = 1.


y = 2 -----> x = 8.


<U>Answer</U>. The solutions are x=1 and x=8.