Question 810579
x^(1/2) - x ^(1/4) - 2 = 0 

{{{x^(1/2) -x^(1/4) - 2 = 0}}}

You raise each term by a power of four, like so:

{{{(x^(1/2))^4 (-x^(1/4))^4 -2^4 = 0^4}}}

The equation becomes:

{{{x^2 + x + 16 = 0}}}

...and just from me to you, I don't think that equation has any roots; SEE:

from {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

a= 1; b= 1; c=16
Substitute
{{{(-1 +- sqrt( 1^2-4*1*16 ))/(2*1) }}}

{{{(-1 +- sqrt( -63 ))/2 }}}

...and personally, I don't think that

{{{sqrt(-63)}}} will give anything besides a "MA ERROR".