What is the answer to x=(x+3)^{1/2} ?

The answer to x=(x+3)^{1/2} is x=(1+13^{1/2})/2

Solve for x: x=(x+3)^{1/2}

The solution is x=(1+13^{1/2})/2

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x = (x + 3)^{\frac{1}{2}}

x = \frac{1 + 1 3 ^{\frac{1}{2}}}{2}

Decimal Notation

x = 2.30277 \dots

Solution steps

x = (x + 3)^{\frac{1}{2}}

Square both sides:

x^{2} = x + 3

x^{2} = x + 3

Solve

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

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

Verify Solutions:

x = \frac{1 + 1 3 ^{\frac{1}{2}}}{2}

True

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

False

The solution is

x = \frac{1 + 1 3 ^{\frac{1}{2}}}{2}

x^{2} - 5 x + 5 = x

x \cdot (x - 1) = 0

2 x + 21 - 2 x + 12 = 1

(11 - 6)^{2} + x = 32

3 (x - 1)^{\frac{1}{3}} = 1

What is the answer to x=(x+3)^{1/2} ?
The answer to x=(x+3)^{1/2} is x=(1+13^{1/2})/2
Solve for x: x=(x+3)^{1/2}
The solution is x=(1+13^{1/2})/2