What is the answer to (φ+1)/φ =φ ?

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

Solve for φ: (φ+1)/φ =φ

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

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\frac{φ + 1}{φ} = φ

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

Decimal Notation

φ = 1.61803 \dots, φ = - 0.61803 \dots

Solution steps

\frac{φ + 1}{φ} = φ

Multiply both sides by

φ

φ + 1 = φ^{2}

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

φ = 0

Combine undefined points with solutions:

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

\frac{1}{1 - x} = 0

\frac{3}{1 - \frac{2}{z}} = 3 z

\frac{x}{x - 7} = \frac{7}{x - 7} + 8

\frac{x + 4}{x - 2} = 3

\frac{15}{x} = - 5

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