What is the answer to 2x^{1/2}-5x^{1/4}=3 ?

The answer to 2x^{1/2}-5x^{1/4}=3 is x=81

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2x^{1/2}-5x^{1/4}=3

2 x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} = 3

x = 81

Solution steps

2 x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} = 3

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} - 5 x^{\frac{1}{4}} = 3

Rewrite the equation with

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

2 u^{2} - 5 u = 3

Solve

2 u^{2} - 5 u = 3 : u = 3, u = - \frac{1}{2}

u = 3, u = - \frac{1}{2}

Substitute back

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

solve for

x

Solve

x^{\frac{1}{4}} = 3 : x = 81

Solve

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

No Solution for

x \in R

x = 81

Verify Solutions:

x = 81

True

The solution is

x = 81

x + 3 = 2 x - 1

8 x - 13 = 1

x + 18 = x - 2

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

2 x + 66 + 20 = 28

What is the answer to 2x^{1/2}-5x^{1/4}=3 ?
The answer to 2x^{1/2}-5x^{1/4}=3 is x=81
Solve for x: 2x^{1/2}-5x^{1/4}=3
The solution is x=81