# How do you solve #x^(3/2) -2x^(3/4) +1 = 0#?

##### 1 Answer

Jan 25, 2017

#### Explanation:

Let

Then:

#x^(3/2) = x^(3/4*2) = (x^(3/4))^2 = t^2#

and our equation becomes:

#0 = t^2-2t+1 = (t-1)^2#

This has one (repeated) root, namely

So:

#x^(3/4) = 1#

If

#x = x^1 = x^(3/4*4/3) = (x^(3/4))^(4/3) = 1^(4/3) = 1#

This is the only Real root.