Question

(y-3) ^2 + 3 (y+2) (y-2)= 9+4y^2 Поняла что по формулам, а дальше не могу. Помогите! Вот мое решение. Где будет восклицательный знак, то и есть место, откуда дальше не могу решить. y^2 - 2-3y+9+3×y^2 - 4=9+4y^2 y^2 - 6y+3y^2 - 4y=9-9+4 4y^2 - 10y=4 ! И если увидите ошибку, подскажите пожалуйста, как правильно.

Answer 1

Я начала решать пример заново, потому что у вас не правильно изначально он был решён)))

Answer 2

Solving the Equation

To solve the equation (y-3)^2 + 3(y+2) + (y-2) = 9 + 4y^2, let's simplify and solve step by step.

1. Expand the squared term (y-3)^2: - (y-3)^2 = (y-3)(y-3) = y^2 - 6y + 9.

2. Distribute the coefficient 3 to the terms inside the parentheses (y+2): - 3(y+2) = 3y + 6.

3. Now, substitute the simplified expressions back into the equation: - y^2 - 6y + 9 + 3y + 6 + (y-2) = 9 + 4y^2.

4. Combine like terms on both sides of the equation: - y^2 - 6y + 3y + y + 9 + 6 - 2 = 9 + 4y^2. - Simplifying further, we get: y^2 - 2y + 13 = 9 + 4y^2.

5. Move all terms to one side of the equation to set it equal to zero: - 0 = 4y^2 - y^2 + 2y - 9 + 13. - Simplifying further, we get: 0 = 3y^2 + 2y + 4.

Solving the Quadratic Equation

To solve the quadratic equation 3y^2 + 2y + 4 = 0, we can use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 3, b = 2, and c = 4.

1. Substitute the values into the quadratic formula: - y = (-2 ± √(2^2 - 4 * 3 * 4)) / (2 * 3). - Simplifying further, we get: y = (-2 ± √(4 - 48)) / 6.

2. Calculate the discriminant (b^2 - 4ac): - (2^2 - 4 * 3 * 4) = 4 - 48 = -44.

Since the discriminant is negative, the quadratic equation has no real solutions. Therefore, there are no real values of y that satisfy the equation (y-3)^2 + 3(y+2) + (y-2) = 9 + 4y^2.

Please note that there might be an error in your calculations, as the equation does not have a solution. Double-check your work to ensure accuracy.