What are the solutions to the equation y^2-5y+1=0 ?

The solutions to the equation y^2-5y+1=0 are y=(5+sqrt(21))/2 ,y=(5-sqrt(21))/2

Find the zeros of y^2-5y+1=0

The zeros of y^2-5y+1=0 are y=(5+sqrt(21))/2 ,y=(5-sqrt(21))/2

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y^{2} - 5 y + 1 = 0

y = \frac{5 + 21}{2}, y = \frac{5 - 21}{2}

Decimal Notation

y = 4.79128 \dots, y = 0.20871 \dots

Solution steps

y^{2} - 5 y + 1 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

(- 5)^{2} - 4 \cdot 1 \cdot 1 = 21

y_{1, 2} = \frac{- ( - 5 ) \pm 21}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 5 ) + 21}{2 \cdot 1}, y_{2} = \frac{- ( - 5 ) - 21}{2 \cdot 1}

y = \frac{- ( - 5 ) + 21}{2 \cdot 1} : \frac{5 + 21}{2}

y = \frac{- ( - 5 ) - 21}{2 \cdot 1} : \frac{5 - 21}{2}

The solutions to the quadratic equation are:

y = \frac{5 + 21}{2}, y = \frac{5 - 21}{2}

x^{2} + 8 x - 40 = 0

8 y^{2} + y + 2 = 0

- 20 x^{2} = - 7 x - 6

x^{2} + 7 x = 32

6 x^{2} - 4 x - 8 = 0

What are the solutions to the equation y^2-5y+1=0 ?
The solutions to the equation y^2-5y+1=0 are y=(5+sqrt(21))/2 ,y=(5-sqrt(21))/2
Find the zeros of y^2-5y+1=0
The zeros of y^2-5y+1=0 are y=(5+sqrt(21))/2 ,y=(5-sqrt(21))/2