What is the answer to 1/φ =φ-1 ?

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

Solve for φ: 1/φ =φ-1

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

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\frac{1}{φ} = φ - 1

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

Decimal Notation

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

Solution steps

\frac{1}{φ} = φ - 1

Multiply both sides by

φ

1 = φ^{2} - φ

Solve

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

\frac{2}{5} = \frac{20}{x}

\frac{4}{x} = \frac{1}{5}

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

\frac{8}{x} = - \frac{4}{7}

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