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

The answer to 1-sqrt(x)=(x-1)^2 is x=0,x=1,x=(3-sqrt(5))/2

Solve for x: 1-sqrt(x)=(x-1)^2

The solution is x=0,x=1,x=(3-sqrt(5))/2

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1 - x = (x - 1)^{2}

x = 0, x = 1, x = \frac{3 - 5}{2}

Solution steps

1 - x = (x - 1)^{2}

Remove square roots

x = x^{4} - 4 x^{3} + 4 x^{2}

Solve

x = x^{4} - 4 x^{3} + 4 x^{2} : x = 0, x = 1, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

x = 0, x = 1, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Verify Solutions:

x = 0

True

, x = 1

True

, x = \frac{3 + 5}{2}

False

, x = \frac{3 - 5}{2}

True

The solutions are

x = 0, x = 1, x = \frac{3 - 5}{2}

2 (x + 1) = 3 - x + 2

2 x + x = 1

7 x = 12 + x

x - 3 + 3 = 2

2 - 2 x = 3 x + 5

What is the answer to 1-sqrt(x)=(x-1)^2 ?
The answer to 1-sqrt(x)=(x-1)^2 is x=0,x=1,x=(3-sqrt(5))/2
Solve for x: 1-sqrt(x)=(x-1)^2
The solution is x=0,x=1,x=(3-sqrt(5))/2