SOLUTION: solve {{{ x^(2/3)-2x^(1/3)-8=0 }}}

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Question 367310: solve
+x%5E%282%2F3%29-2x%5E%281%2F3%29-8=0+
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Let z=x%5E%281%2F3%29%5E%22%22. So z%5E2=x%5E%282%2F3%29%5E%22%22


So the equation then becomes z%5E2-2z-8=0.


Solve for 'z' and then use those solutions to find the solutions in terms of 'x'.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E%282%2F3%29-2x%5E%281%2F3%29-8=0+
Let 1%2F3+=+z
+x%5E%282z%29-2x%5Ez-8=0+
x%5E%282z%29+-+2x%5Ez+%2B+1+=+8+%2B+1
%28x%5Ez+-+1%29%5E2+=+9
x%5Ez+-+1+=+3
x%5Ez+=+4
Take the zth root of both sides
x+=+4%5E%281%2Fz%29
Since z+=+1%2F3,
x+=+4%5E3
x+=+64