What are the solutions to the equation y^2-y-1=0 ?

The solutions to the equation y^2-y-1=0 are y=(1+sqrt(5))/2 ,y=(1-sqrt(5))/2

Find the zeros of y^2-y-1=0

The zeros of y^2-y-1=0 are y=(1+sqrt(5))/2 ,y=(1-sqrt(5))/2

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y^{2} - y - 1 = 0

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

Decimal Notation

y = 1.61803 \dots, y = - 0.61803 \dots

Solution steps

y^{2} - y - 1 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

3 x^{2} - 12 x = 0

x, x^{2} + y^{2} - 4 x - 2 y + 9 = 0

x^{2} + 3 x - 4 = 0

x^{2} + x + 1 = 13

(2 x + 1) x = 0

What are the solutions to the equation y^2-y-1=0 ?
The solutions to the equation y^2-y-1=0 are y=(1+sqrt(5))/2 ,y=(1-sqrt(5))/2
Find the zeros of y^2-y-1=0
The zeros of y^2-y-1=0 are y=(1+sqrt(5))/2 ,y=(1-sqrt(5))/2