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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Decimal Notation

x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

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

Cross multiply

1 + x = x^{2}

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

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

\frac{5}{3 x - 4} = \frac{- 3}{1 - 2 x}

G (x) = - \frac{8}{x - 5}

y, x = \frac{y}{( y - 2 )}

\frac{8}{5} = \frac{24}{x}

3 = \frac{7}{a - 6}

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