Question

(3y+1)²= -27 = (4y + 9)(4y – 9) +2(5y + 2)(2y-7) ​

Answer 1

Ответ:

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Объяснение:

Answer 2

Let's solve the given equation step by step.

First, let's simplify the equation (3y + 1)² = -27:

(3y + 1)² = -27 9y² + 6y + 1 = -27 9y² + 6y + 28 = 0

Next, let's factorize the quadratic equation 9y² + 6y + 28 = 0:

Using the quadratic formula: y = (-b ± √(b² - 4ac)) / (2a)

For the equation 9y² + 6y + 28 = 0, the coefficients are: a = 9, b = 6, c = 28

Plugging these values into the quadratic formula:

y = (-6 ± √(6² - 4 * 9 * 28)) / (2 * 9) y = (-6 ± √(36 - 1008)) / 18 y = (-6 ± √(-972)) / 18 y = (-6 ± √(972) * √(-1)) / 18 y = (-6 ± 18i√(3)) / 18

Simplifying further:

y = (-6/18) ± (18i√(3)) / 18 y = (-1/3) ± i√(3)

Therefore, the solutions to the equation (3y + 1)² = -27 are: y = (-1/3) + i√(3) y = (-1/3) - i√(3)

Moving on to the second equation:

(4y + 9)(4y - 9) + 2(5y + 2)(2y - 7)

Using the distributive property:

(16y² - 81) + 2(10y² - 34y - 14)

Simplifying further:

16y² - 81 + 20y² - 68y - 28 36y² - 68y - 109

Therefore, the simplified form of the equation (4y + 9)(4y - 9) + 2(5y + 2)(2y - 7) is 36y² - 68y - 109.

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