What is the answer to y^{1/2}-9y^{1/4}+20=0 ?

The answer to y^{1/2}-9y^{1/4}+20=0 is y=625,y=256

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y^{1/2}-9y^{1/4}+20=0

y^{\frac{1}{2}} - 9 y^{\frac{1}{4}} + 20 = 0

y = 625, y = 256

Solution steps

y^{\frac{1}{2}} - 9 y^{\frac{1}{4}} + 20 = 0

Use the following exponent property

: a^{\frac{1}{n}} = (a^{\frac{1}{m}})^{\frac{m}{n}}

y^{\frac{1}{2}} = (y^{\frac{1}{4}})^{\frac{4}{2}}

(y^{\frac{1}{4}})^{2} - 9 y^{\frac{1}{4}} + 20 = 0

Rewrite the equation with

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

u^{2} - 9 u + 20 = 0

Solve

u^{2} - 9 u + 20 = 0 : u = 5, u = 4

u = 5, u = 4

Substitute back

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

solve for

y

Solve

y^{\frac{1}{4}} = 5 : y = 625

Solve

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

y = 625, y = 256

Verify Solutions:

y = 625

True

, y = 256

True

The solutions are

y = 625, y = 256

10 - 11 x = x - 1

8 = 13 - 16 - 9 x

x - 1 + x - 4 = x + 4

2 x + 3 + x + 3 = 0

8 x + 6 - 3 2 x - 1 = 0

What is the answer to y^{1/2}-9y^{1/4}+20=0 ?
The answer to y^{1/2}-9y^{1/4}+20=0 is y=625,y=256
Solve for y: y^{1/2}-9y^{1/4}+20=0
The solution is y=625,y=256