What is the answer to x^{1/2}-5x^{1/4}+6=0 ?

The answer to x^{1/2}-5x^{1/4}+6=0 is x=81,x=16

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

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

x = 81, x = 16

Solution steps

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

Rewrite the equation with

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

u^{2} - 5 u + 6 = 0

Solve

u^{2} - 5 u + 6 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 81, x = 16

Verify Solutions:

x = 81

True

, x = 16

True

The solutions are

x = 81, x = 16

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

- 10 + 7 p = p

x^{2} + 2 x + x^{2} + 2 x + 10 - 20 = 0

2624 x^{2} + 1240 x + 25600 = 260

What is the answer to x^{1/2}-5x^{1/4}+6=0 ?
The answer to x^{1/2}-5x^{1/4}+6=0 is x=81,x=16
Solve for x: x^{1/2}-5x^{1/4}+6=0
The solution is x=81,x=16