(y + 5)(y² + 6y + 10) =
Answers
(y^2 -6y)^2 - 4(y^2 -6y + 3) - 20 = 0
Let y^2 -6y = x ——> 1
x^2 - 4(x + 3) - 20 = 0
x^2 - 4x - 12 - 20 = 0
x^2 - 4x - 32 = 0
x^2 - 8x + 4x - 32 = 0
x(x - 8) + 4(x - 8) = 0
(x + 4)(x - 8) = 0
x + 4 = 0, x - 8 = 0
x = -4, x = 8
Substitute x = -4 in equation 1,
y^2 -6y = -4
y^2 -6y + 4 = 0
y = (-(-6) +/- sqrt(36 - 16))/2
y = (6 +/- sqrt(20))/2
y = (6 +/- 2*sqrt(5))/2
y = 3 +/- sqrt(5)
y = 3 + sqrt(5), 3 - sqrt(5)
Substitute x = 8 in equation 1,
y^2 -6y = 8
y^2 -6y - 8 = 0
y = (-(-6) +/- sqrt(64 + 32))/2
y = (-(-6) +/- sqrt(96))/2
y = (-(-6) +/- 4*sqrt(6))/2
y = 3 +/- 2*sqrt(6)
y = 3 + 2*sqrt(6), 3 - 2*sqrt(6)
Therefore
y = 3 + sqrt(5), 3 - sqrt(5), 3 + 2*sqrt(6), 3 - 2*sqrt(6) ——> Answer
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Step-by-step explanation:
(y^2 -6y)^2 - 4(y^2 -6y + 3) - 20 = 0
Let y^2 -6y = x ——> 1
x^2 - 4(x + 3) - 20 = 0
x^2 - 4x - 12 - 20 = 0
x^2 - 4x - 32 = 0
x^2 - 8x + 4x - 32 = 0
x(x - 8) + 4(x - 8) = 0
(x + 4)(x - 8) = 0
x + 4 = 0, x - 8 = 0
x = -4, x = 8
Substitute x = -4 in equation 1,
y^2 -6y = -4
y^2 -6y + 4 = 0
y = (-(-6) +/- sqrt(36 - 16))/2
y = (6 +/- sqrt(20))/2
y = (6 +/- 2*sqrt(5))/2
y = 3 +/- sqrt(5)
y = 3 + sqrt(5), 3 - sqrt(5)
Substitute x = 8 in equation 1,
y^2 -6y = 8
y^2 -6y - 8 = 0
y = (-(-6) +/- sqrt(64 + 32))/2
y = (-(-6) +/- sqrt(96))/2
y = (-(-6) +/- 4*sqrt(6))/2
y = 3 +/- 2*sqrt(6)
y = 3 + 2*sqrt(6), 3 - 2*sqrt(6)
Therefore
y = 3 + sqrt(5), 3 - sqrt(5), 3 + 2*sqrt(6), 3 - 2*sqrt(6) ——> Answer