SOLUTION: Thank you in advance for help with this equation. x^2/3+x^1/3-2=0

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Question 144549This question is from textbook
: Thank you in advance for help with this equation. x^2/3+x^1/3-2=0 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%282%2F3%29%2Bx%5E%281%2F3%29-2=0 Start with the given equation

Let u=x%5E%281%2F3%29

u%5E2%2Bu-2=0 Plug in u=x%5E%281%2F3%29

%28u%2B2%29%28u-1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
u%2B2=0 or u-1=0

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

Remember, we let u=x%5E%281%2F3%29


x%5E%281%2F3%29=-2 or x%5E%281%2F3%29=1 Replace "u" with x%5E%281%2F3%29


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