Question 829436
Let {{{u=x^(1/3)}}}
{{{9x^(2/3)+4x^(-2/3)=37}}}
Mutliply both sides by {{{x^(2/3)}}}
{{{9x^(4/3)+4=37x^(2/3)}}}
{{{9x^(4/3)-37x^(2/3)+4=0}}}
Substitute {{{u=x^(2/3)}}}
{{{9u^2-37u+4=0}}}
{{{(9u-1)(u-4)=0}}}
Two solutions:
{{{9u-1=0}}}
{{{9u=1}}}
{{{u=1/9}}}
{{{x^(2/3)=1/9}}}
{{{highlight(x=1/27)}}}
and
{{{u-4=0}}}
{{{u=4}}}
{{{x^(2/3)=4}}}
{{{x=4^(3/2)}}}
{{{highlight(x=8)}}}
Now check the solution in the original equation to verify that it works.