What is the answer to x^{1/2}-7x^{1/4}+12=0 ?

The answer to x^{1/2}-7x^{1/4}+12=0 is x=256,x=81

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x^{1/2}-7x^{1/4}+12=0

x^{\frac{1}{2}} - 7 x^{\frac{1}{4}} + 12 = 0

x = 256, x = 81

Solution steps

x^{\frac{1}{2}} - 7 x^{\frac{1}{4}} + 12 = 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} - 7 x^{\frac{1}{4}} + 12 = 0

Rewrite the equation with

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

u^{2} - 7 u + 12 = 0

Solve

u^{2} - 7 u + 12 = 0 : u = 4, u = 3

u = 4, u = 3

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 256, x = 81

Verify Solutions:

x = 256

True

, x = 81

True

The solutions are

x = 256, x = 81

5 3 x - 3 - 5 4 x - 7 = 0

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

y, 5 x y - 2 y - 3 x = 0

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

x - 1 + x - 7 = 2 x - 3

What is the answer to x^{1/2}-7x^{1/4}+12=0 ?
The answer to x^{1/2}-7x^{1/4}+12=0 is x=256,x=81
Solve for x: x^{1/2}-7x^{1/4}+12=0
The solution is x=256,x=81