What are the solutions to the equation x(x-1)=1 ?

The solutions to the equation x(x-1)=1 are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Find the zeros of x(x-1)=1

The zeros of x(x-1)=1 are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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x (x - 1) = 1

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

Decimal Notation

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

Solution steps

x (x - 1) = 1

Expand

x (x - 1) : x^{2} - x

x^{2} - x = 1

Move

1

to the left side

x^{2} - x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 1)^{2} - 4 \cdot 1 \cdot (- 1) = 5

x_{1, 2} = \frac{- ( - 1 ) \pm 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 5}{2 \cdot 1}, x_{2} = \frac{- ( - 1 ) - 5}{2 \cdot 1}

x = \frac{- ( - 1 ) + 5}{2 \cdot 1} : \frac{1 + 5}{2}

x = \frac{- ( - 1 ) - 5}{2 \cdot 1} : \frac{1 - 5}{2}

The solutions to the quadratic equation are:

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

x^{2} - x - 12 = 0

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

2 x - 3 x^{2} = 5

(3 x + 2)^{2} = 4

x^{2} - 9 x + 15 = 0

What are the solutions to the equation x(x-1)=1 ?
The solutions to the equation x(x-1)=1 are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of x(x-1)=1
The zeros of x(x-1)=1 are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2