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

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

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

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

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a^{2} - a - 1 = 0

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

Decimal Notation

a = 1.61803 \dots, a = - 0.61803 \dots

Solution steps

a^{2} - a - 1 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

\frac{1}{2 2}

8 x - 4 + 3 x = 7 x + x + 14

14 x = - 12 x

8 w^{2} = 50

1.5 t^{2} + 5.83 t - 4.1 = 0

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