Question 907343
{{{x-sqrt(6-x)=4}}}
{{{x-4=sqrt(6-x)}}}
{{{(x-4)^2=6-x}}}
{{{x^2-8x+16=6-x}}}
{{{x^2-7x+10=0}}}
{{{(x-2)(x-5)=0}}}
Two solutions:
{{{x-2=0}}}
{{{x=2}}}
and
{{{x-5=0}}}
{{{x=5}}}
Verify the solutions.
{{{2-sqrt(6-2)=4}}}
{{{2-sqrt(4)=4}}}
{{{2-2=4}}}
{{{0=4}}}
Not a solution.
{{{5-sqrt(6-5)=4}}
{{{5-sqrt(1)=4}}}
{{{5-1=4}}}
{{{4=4}}}
Good solution.
{{{highlight(x=5)}}}
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.
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{{{x^(1/3) – 36 = 9x^(1/6)}}}
{{{x^(1/3)- 9x^(1/6)-36=0}}}
Substitute,
{{{t=x^(1/6)}}}
{{{t^2=x^(1/3)}}}
{{{highlight(t^2-9t-36=0)}}}
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.
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{{{u=x^4}}}
{{{16=x^4}}}
{{{highlight(x=2)}}} and {{{highlight(x=-2)}}}
and
{{{x^4=-4}}}
I'm assuming you aren't looking for complex solutions but only real solutions. 
There are no real solutions.