What is the answer to x^{1/2}-6x^{1/4}+8=0 ?

The answer to x^{1/2}-6x^{1/4}+8=0 is x=256,x=16

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x^{1/2}-6x^{1/4}+8=0

x^{\frac{1}{2}} - 6 x^{\frac{1}{4}} + 8 = 0

x = 256, x = 16

Solution steps

x^{\frac{1}{2}} - 6 x^{\frac{1}{4}} + 8 = 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} - 6 x^{\frac{1}{4}} + 8 = 0

Rewrite the equation with

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

u^{2} - 6 u + 8 = 0

Solve

u^{2} - 6 u + 8 = 0 : u = 4, u = 2

u = 4, u = 2

Substitute back

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

solve for

x

Solve

x^{\frac{1}{4}} = 4 : x = 256

Solve

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

x = 256, x = 16

Verify Solutions:

x = 256

True

, x = 16

True

The solutions are

x = 256, x = 16

2 x - 2 x + 2 = 0

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

4 x - 3 = - 1

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

4 x - 3 - x - 2 = 3 x - 5

What is the answer to x^{1/2}-6x^{1/4}+8=0 ?
The answer to x^{1/2}-6x^{1/4}+8=0 is x=256,x=16
Solve for x: x^{1/2}-6x^{1/4}+8=0
The solution is x=256,x=16