Question 647659
ok let assume 


{{{ y = x^(1/3) }}}.....1 

then 

{{{ x^(1/3) - 2x^(-1/3) = 1 }}} .....1 
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{{{ x^(1/3) - 2x^(-1/3) = 1 }}} .....1 ...solve for {{{x}}}..

note, because {{{a^(-n) }}}means {{{1/a^n}}} we will have

{{{ 1/x^3 - 2(1/x^3) = 1 }}}  .......then replace {{{x^1/3}}} with {{{y}}}
then you get


{{{ y - 2(1/y) = 1 }}}.........simplify

{{{ (y^2 - 2)/y = 1 }}}

{{{ y^2 - 2 = y }}}

{{{ y^2 -y- 2 = 0 }}}...from this we can get

{{{(y-2) (y+1) = 0}}}

we can get value of {{{y}}} from {{{y-2 = 0}}} then {{{y = 2}}} 

and from {{{y+1 = 0}}} then {{{y = -1}}}

 continue to put the value of {{{y}}} to {{{x}}}

{{{y = x^1/3}}}

assume {{{y = 2}}}

{{{x^1/3 = 2}}} -> {{{x = 2^3}}} -> {{{highlight(x = 8)}}}

assume {{{y = -1}}}

{{{x^1/3 = -1}}} -> {{{x = -1^3}}} -> {{{highlight(x = -1)}}}