What are the solutions to the equation (1-y)(3-y)(6-y)=-70 ?

The solutions to the equation (1-y)(3-y)(6-y)=-70 are y=8,y=1+sqrt(10)i,y=1-sqrt(10)i

Find the zeros of (1-y)(3-y)(6-y)=-70

The zeros of (1-y)(3-y)(6-y)=-70 are y=8,y=1+sqrt(10)i,y=1-sqrt(10)i

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(1 - y) (3 - y) (6 - y) = - 70

y = 8, y = 1 + 10 i, y = 1 - 10 i

Solution steps

(1 - y) (3 - y) (6 - y) = - 70

Expand

(1 - y) (3 - y) (6 - y) : 18 - 27 y + 10 y^{2} - y^{3}

18 - 27 y + 10 y^{2} - y^{3} = - 70

Move

70

to the left side

- y^{3} + 10 y^{2} - 27 y + 88 = 0

Factor

- y^{3} + 10 y^{2} - 27 y + 88 : - (y - 8) (y^{2} - 2 y + 11)

- (y - 8) (y^{2} - 2 y + 11) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - 8 = 0 or y^{2} - 2 y + 11 = 0

Solve

y - 8 = 0 : y = 8

Solve

y^{2} - 2 y + 11 = 0 : y = 1 + 10 i, y = 1 - 10 i

The solutions are

y = 8, y = 1 + 10 i, y = 1 - 10 i

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

2 x^{3} - 2 x^{2} + 5 = 0

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

20 x^{25} = 25 x^{20}

125 = m^{3}

What are the solutions to the equation (1-y)(3-y)(6-y)=-70 ?
The solutions to the equation (1-y)(3-y)(6-y)=-70 are y=8,y=1+sqrt(10)i,y=1-sqrt(10)i
Find the zeros of (1-y)(3-y)(6-y)=-70
The zeros of (1-y)(3-y)(6-y)=-70 are y=8,y=1+sqrt(10)i,y=1-sqrt(10)i