What is the answer to y^2-sqrt(8y)=sqrt(18y)-1 ?

The answer to y^2-sqrt(8y)=sqrt(18y)-1 is y\approx 0.02001…,y\approx 3.49583…

Solve for y: y^2-sqrt(8y)=sqrt(18y)-1

The solution is y\approx 0.02001…,y\approx 3.49583…

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y^{2} - 8 y = 18 y - 1

y \approx 0.02001 \dots, y \approx 3.49583 \dots

Solution steps

y^{2} - 8 y = 18 y - 1

Remove square roots

72 y^{5} + 144 y^{3} + 72 y = y^{8} + 4 y^{6} + 20 y^{5} + 6 y^{4} + 40 y^{3} + 104 y^{2} + 20 y + 1

Switch sides

- 2 18 y y^{2} + 2 y^{2} + y^{4} + 18 y - 2 18 y + 1 = 8 y

Move

2 y^{2}

to the right side

- 2 18 y y^{2} + y^{4} + 18 y - 2 18 y + 1 = 8 y - 2 y^{2}

Move

y^{4}

to the right side

- 2 18 y y^{2} + 18 y - 2 18 y + 1 = 8 y - 2 y^{2} - y^{4}

Move

18 y

to the right side

- 2 18 y y^{2} - 2 18 y + 1 = - y^{4} - 2 y^{2} - 10 y

Move

1

to the right side

- 2 18 y y^{2} - 2 18 y = - y^{4} - 2 y^{2} - 10 y - 1

Factor

- 2 18 y y^{2} - 2 18 y : - 2 18 y (y^{2} + 1)

- 2 18 y (y^{2} + 1) = - y^{4} - 2 y^{2} - 10 y - 1

Solve

72 y^{5} + 144 y^{3} + 72 y = y^{8} + 4 y^{6} + 20 y^{5} + 6 y^{4} + 40 y^{3} + 104 y^{2} + 20 y + 1 : y \approx 0.02001 \dots, y \approx 3.49583 \dots

y \approx 0.02001 \dots, y \approx 3.49583 \dots

Verify Solutions:

y \approx 0.02001 \dots

True

, y \approx 3.49583 \dots

True

The solutions are

y \approx 0.02001 \dots, y \approx 3.49583 \dots

5 x - 6 = - 20

x - 3 + x + 2 = 5

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

x - 9 = 7

x - 9 = 6

What is the answer to y^2-sqrt(8y)=sqrt(18y)-1 ?
The answer to y^2-sqrt(8y)=sqrt(18y)-1 is y\approx 0.02001…,y\approx 3.49583…
Solve for y: y^2-sqrt(8y)=sqrt(18y)-1
The solution is y\approx 0.02001…,y\approx 3.49583…