What is the answer to x=sqrt(x)+1 ?

The answer to x=sqrt(x)+1 is x=(3+sqrt(5))/2

Solve for x: x=sqrt(x)+1

The solution is x=(3+sqrt(5))/2

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x = x + 1

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

Solution steps

x = x + 1

Remove square roots

x^{2} - 2 x + 1 = x

Solve

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

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

Verify Solutions:

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

True

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

False

The solution is

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

2 x + 3 - x = 2

x + 8 - x + 2 = 1

x + 8 = 2 x + 5

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