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

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

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

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

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x = 1 - \frac{1}{x + 1}

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

Decimal Notation

x = 0, x = - 0.61803 \dots

Solution steps

x = 1 - \frac{1}{x + 1}

Multiply both sides by

x + 1

x x + 1 = 1 \cdot x + 1 - \frac{1}{x + 1} x + 1

Simplify

x x + 1 = x + 1 - 1

Move

x + 1

to the left side

x x + 1 - x + 1 = - 1

Factor

x x + 1 - x + 1 : x + 1 (x - 1)

x + 1 (x - 1) = - 1

Divide both sides by

x - 1

x + 1 = - \frac{1}{x - 1}

Square both sides:

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

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

Solve

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

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

Verify Solutions:

x = 0

True

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

False

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

True

The solutions are

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

y^{\frac{3}{2}} = 8

2 x + 3 - 3 = 0

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

3 x + 4 = 3 x + 4

x^{\frac{5}{2}} = 0

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