Question 1037741
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X^1/2-3x^1/4+2=0.
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<pre>
Introduce a new unknown p = {{{x^(1/4)}}}.
Then {{{x^(1/2)}}} = {{{p^2}}}, and your equation takes the form

{{{p^2 - 3p + 2}}} = {{{0}}}.

Factor left side. You will get

(p-1)*(p-2) = 0.

The roots are p=1  or/and  p=2.

Since p = {{{x^(1/4)}}}, it means that  

{{{x^(1/4)}}} = 1     (1)

or/and  

{{{x^(1/4)}}} = 2.    (2)

Raise 1) and (2) into degree 4. you will get the solutions of the original problem

x = 1  or/and  x = {{{2^4}}} = 16.

<U>Answer</U>.  x = 1  or/and  x = 16.
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