What is the answer to (sqrt(y)-1)^2=5-sqrt(y) ?

The answer to (sqrt(y)-1)^2=5-sqrt(y) is y=(9+sqrt(17))/2

Solve for y: (sqrt(y)-1)^2=5-sqrt(y)

The solution is y=(9+sqrt(17))/2

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(y - 1)^{2} = 5 - y

y = \frac{9 + 17}{2}

Decimal Notation

y = 6.56155 \dots

Solution steps

(y - 1)^{2} = 5 - y

Remove square roots

16 y^{3} - 128 y^{2} + 256 y = y^{4} - 10 y^{3} + 57 y^{2} - 160 y + 256

Move

y^{2}

to the right side

- 4 y y - 4 y + 16 y + 16 = y - y^{2}

Move

4 y

to the right side

- 4 y y + 16 y + 16 = - y^{2} + 5 y

Move

16

to the right side

- 4 y y + 16 y = - y^{2} + 5 y - 16

Factor

- 4 y y + 16 y : 4 y (- y + 4)

4 y (- y + 4) = - y^{2} + 5 y - 16

Solve

16 y^{3} - 128 y^{2} + 256 y = y^{4} - 10 y^{3} + 57 y^{2} - 160 y + 256 : y = 1, y = 16, y = \frac{9 + 17}{2}, y = \frac{9 - 17}{2}

y = 1, y = 16, y = \frac{9 + 17}{2}, y = \frac{9 - 17}{2}

Verify Solutions:

y = 1

False

, y = 16

False

, y = \frac{9 + 17}{2}

True

, y = \frac{9 - 17}{2}

False

The solution is

y = \frac{9 + 17}{2}

x - 16 x + 60 = 0

3 + 7 x - 13 = x

0 = 11 x^{2} + 0

- 4 + 3 x + 52 = x

What is the answer to (sqrt(y)-1)^2=5-sqrt(y) ?
The answer to (sqrt(y)-1)^2=5-sqrt(y) is y=(9+sqrt(17))/2
Solve for y: (sqrt(y)-1)^2=5-sqrt(y)
The solution is y=(9+sqrt(17))/2