Question 144549
{{{x^(2/3)+x^(1/3)-2=0}}} Start with the given equation


Let {{{u=x^(1/3)}}}


{{{u^2+u-2=0}}} Plug in {{{u=x^(1/3)}}}


{{{(u+2)(u-1)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{u+2=0}}} or  {{{u-1=0}}} 


{{{u=-2}}} or  {{{u=1}}}    Now solve for u in each case


Remember, we let {{{u=x^(1/3)}}}



{{{x^(1/3)=-2}}} or  {{{x^(1/3)=1}}} Replace "u" with  {{{x^(1/3)}}}



{{{x=-8}}} or {{{x=1}}} Cube both sides in each case



Notice that when you plug in {{{x=-8}}} you don't get the correct answer. So {{{x=-8}}} is an extraneous solution. 




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Answer:


So the solution is {{{x=1}}}