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

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Answer 1 · 2017-01-25T19:52:14

$x=1$

Let $t = x^(3/4)$

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 $t=1$

So:

$x^(3/4) = 1$

If $x >= 0$ then:

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

This is the only Real root.

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