What is the answer to x=(x+1)^{1/2} ?

The answer to x=(x+1)^{1/2} is x=(1+5^{1/2})/2

Solve for x: x=(x+1)^{1/2}

The solution is x=(1+5^{1/2})/2

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x = (x + 1)^{\frac{1}{2}}

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

Decimal Notation

x = 1.61803 \dots

Solution steps

x = (x + 1)^{\frac{1}{2}}

Square both sides:

x^{2} = x + 1

x^{2} = x + 1

Solve

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

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

Verify Solutions:

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

True

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

False

The solution is

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

10 100 - x = 60 x - 300

5 x - 9 = 4

x^{2} - x - 6 = x + 3

- 9 4 g + 13 = - 45

x = 2 x^{2} - 15

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