SOLUTION: How do you find x^2 if x satisfies (x+9)^(1/3)-(x-9)^(1/3)=3

Question 212297: How do you find x^2 if x satisfies (x+9)^(1/3)-(x-9)^(1/3)=3
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
How do you find if x satisfies
1.


Let  and 

2. 

Cube both sides:

   

Group the first and last terms on the left together

3. 

Notice that 
Substitute  for 



Subtract 18 from both sides:



Divide through by 



Factor out  on the left



Using equation 2 above, the parenthetical expression
equals 3



Divide both sides by 3



Cube both sides:





Substitute  and , 





Add  to both sides:



That's what you wanted.

Edwin

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