x^1/2-5x^1/4+6=0

Question

x to the one half power minus five x to the one fourth power plus six equals zero

Answer 1

x^1/2-5x^1/4+6=0

let u=x^1/4.  The equation now reads

u²-5u+6=0, a quadratic.  Factor it and get

(u-3)(u-2)=0 or u=3, u=2

Solving for x we have x^1/4=3→x=81

x^1/4=2→x=16