What is the answer to x^{1/2}-5x^{1/4}+4=0 ?

The answer to x^{1/2}-5x^{1/4}+4=0 is x=256,x=1

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x^{1/2}-5x^{1/4}+4=0

x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} + 4 = 0

x = 256, x = 1

Solution steps

x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} + 4 = 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} - 5 x^{\frac{1}{4}} + 4 = 0

Rewrite the equation with

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

u^{2} - 5 u + 4 = 0

Solve

u^{2} - 5 u + 4 = 0 : u = 4, u = 1

u = 4, u = 1

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 256, x = 1

Verify Solutions:

x = 256

True

, x = 1

True

The solutions are

x = 256, x = 1

x = 4 - x - 8

4 x + 7 = 2 x - 3 + 8

x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} + 6 = 0

(x - 3) x^{2} - 5 x + 4 = 2 x - 6

- 10 + 7 p = p

What is the answer to x^{1/2}-5x^{1/4}+4=0 ?
The answer to x^{1/2}-5x^{1/4}+4=0 is x=256,x=1
Solve for x: x^{1/2}-5x^{1/4}+4=0
The solution is x=256,x=1