What are the solutions to the equation (y-1)(y-2)= 1/2 y^2 ?

The solutions to the equation (y-1)(y-2)= 1/2 y^2 are y=3+sqrt(5),y=3-sqrt(5)

Find the zeros of (y-1)(y-2)= 1/2 y^2

The zeros of (y-1)(y-2)= 1/2 y^2 are y=3+sqrt(5),y=3-sqrt(5)

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(y - 1) (y - 2) = \frac{1}{2} y^{2}

y = 3 + 5, y = 3 - 5

Decimal Notation

y = 5.23606 \dots, y = 0.76393 \dots

Solution steps

(y - 1) (y - 2) = \frac{1}{2} y^{2}

Multiply both sides by

2

2 (y - 1) (y - 2) = y^{2}

Expand

2 (y - 1) (y - 2) : 2 y^{2} - 6 y + 4

2 y^{2} - 6 y + 4 = y^{2}

Move

y^{2}

to the left side

y^{2} - 6 y + 4 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 4}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot 4 = 25

y_{1, 2} = \frac{- ( - 6 ) \pm 2 5}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 6 ) + 2 5}{2 \cdot 1}, y_{2} = \frac{- ( - 6 ) - 2 5}{2 \cdot 1}

y = \frac{- ( - 6 ) + 2 5}{2 \cdot 1} : 3 + 5

y = \frac{- ( - 6 ) - 2 5}{2 \cdot 1} : 3 - 5

The solutions to the quadratic equation are:

y = 3 + 5, y = 3 - 5

3 x^{2} - 4 = 2 x - 9

25 x^{2} + 121 = 0

9 x^{2} = 324

s (11 - s) = 24

5 x^{2} - 3 (2 x - 1) = 2 x^{2} - 8 x

What are the solutions to the equation (y-1)(y-2)= 1/2 y^2 ?
The solutions to the equation (y-1)(y-2)= 1/2 y^2 are y=3+sqrt(5),y=3-sqrt(5)
Find the zeros of (y-1)(y-2)= 1/2 y^2
The zeros of (y-1)(y-2)= 1/2 y^2 are y=3+sqrt(5),y=3-sqrt(5)