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

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

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

The solution is x=(1+sqrt(5))/2

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x = 1 + x

x = \frac{1 + 5}{2}

Decimal Notation

x = 1.61803 \dots

Solution steps

x = 1 + x

Square both sides:

x^{2} = 1 + x

x^{2} = 1 + x

Solve

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

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

Verify Solutions:

x = \frac{1 + 5}{2}

True

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

False

The solution is

x = \frac{1 + 5}{2}

2 + x - 4 + 10 - 3 x = 0

(x + 1)^{\frac{4}{3}} = 16

- \frac{1}{4 x ^{\frac{3}{2}}} = 0

4 x + 8 + 8 = 2 x

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