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

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

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

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

x = 1

Solution steps

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

Use the following exponent property

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

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

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

Rewrite the equation with

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

2 u^{2} - u - 1 = 0

Solve

2 u^{2} - u - 1 = 0 : u = 1, u = - \frac{1}{2}

u = 1, u = - \frac{1}{2}

Substitute back

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

solve for

x

Solve

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

Solve

x^{\frac{1}{4}} = - \frac{1}{2} :

No Solution for

x \in R

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

x + 4 + 7 = 5

3 x - 5 = x - 3

x^{2} - 5 = x + 5

x - 5 = 3 x - 11

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