Question 357725
{{{2x^(2/3)-7x^(1/3)=4}}}
This is a quadratic equation in disguise.
Use a substitution, {{{u=x^(1/3)}}}
{{{u^2=x^(2/3)}}}
{{{2u^2-7u=4}}}
{{{2u^2-7u-4=0}}}
{{{(2u+1)(u-4)=0}}}
Two solutions:
{{{2u+1=0}}}
{{{2u=-1}}}
{{{u=-1/2}}}
{{{x^(1/3)=-1/2}}}
{{{highlight(x=-1/8)}}}
.
.
.
{{{u-4=0}}}
{{{u=4}}}
{{{x^(1/3)=4}}}
{{{highlight(x=64)}}}