What is the answer to x^{3/2}-2x^{3/4}+1=0 ?

The answer to x^{3/2}-2x^{3/4}+1=0 is x=1

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x^{3/2}-2x^{3/4}+1=0

x^{\frac{3}{2}} - 2 x^{\frac{3}{4}} + 1 = 0

x = 1

Solution steps

x^{\frac{3}{2}} - 2 x^{\frac{3}{4}} + 1 = 0

Use the following exponent property

: a^{\frac{n}{k}} = (a^{\frac{1}{m}})^{(n \cdot \frac{m}{k})}

x^{\frac{3}{2}} = (x^{\frac{1}{4}})^{(3 \cdot \frac{4}{2})}

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{3}{4}} = (x^{\frac{1}{4}})^{3}

(x^{\frac{1}{4}})^{6} - 2 (x^{\frac{1}{4}})^{3} + 1 = 0

Rewrite the equation with

x^{\frac{1}{4}} = u

u^{6} - 2 u^{3} + 1 = 0

Solve

u^{6} - 2 u^{3} + 1 = 0 : u = 1

u = 1

Substitute back

u = x^{\frac{1}{4}},

solve for

x

Solve

x^{\frac{1}{4}} = 1 : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

u - 8 = 2

x = - 2

2 x + 14 = x + 3

x = 40 - 3 x

x = 14

What is the answer to x^{3/2}-2x^{3/4}+1=0 ?
The answer to x^{3/2}-2x^{3/4}+1=0 is x=1
Solve for x: x^{3/2}-2x^{3/4}+1=0
The solution is x=1