Question

\[2x ^{1/2}-x ^{1/4}=3\]

Answer 1

its really just a quadratic
u = x^1/4
\[2u ^{2}-u-3 =0\]
factor
\[(2u-3)(u+1) = 0\]
u = 3/2, -1
x = u^4
x=(-1)^4 = 1
x = (3/2)^4 = 81/16

check for extraneous solutions
2(1) - 1 not equal 3

solution:
x = 81/16