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

The answer to x^{1/2}-3x^{1/4}+2=0 is x=16,x=1

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

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

x = 16, x = 1

Solution steps

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

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

Rewrite the equation with

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

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

Solve

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

u = 2, u = 1

Substitute back

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

solve for

x

Solve

x^{\frac{1}{4}} = 2 : x = 16

Solve

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

x = 16, x = 1

Verify Solutions:

x = 16

True

, x = 1

True

The solutions are

x = 16, x = 1

x + 5 + 1 = 2 x

x - 3 = 1 + x - 4

x = 10 x

x - 3 + x + 1 = 2

\frac{1}{6} \times 6 x + 6 = x

What is the answer to x^{1/2}-3x^{1/4}+2=0 ?
The answer to x^{1/2}-3x^{1/4}+2=0 is x=16,x=1
Solve for x: x^{1/2}-3x^{1/4}+2=0
The solution is x=16,x=1