Question

Что получиться в итоге не сходиться с ответом надо преобразовать! 2(2-y)^2+(2-y)y+y^2=8 y^2-3y=0 Ответ вот

Answer 1

2(2-y)² + (2-y)y + y² =8
2(4-4y+y²) +2y-y²+y²-8=0
8-8y+2y²+2y-8=0
2y²-6y=0
y²-3y=0
y(y-3)=0

1) y=0
2) y-3=0
    y=3
Ответ: 0;  3.

Answer 2

Solving the Equation

To solve the given equation 2(2-y)^2 + (2-y)y + y^2 = 8 + y^2 - 3y = 0, we can start by simplifying and solving for the value of y.

First, let's simplify the equation step by step:

1. Expand the squared term: - 2(2-y)^2 can be expanded to 2(4 - 4y + y^2), which simplifies to 8 - 8y + 2y^2. 2. Combine like terms: - The equation becomes 8 - 8y + 2y^2 + (2-y)y + y^2 = 8 + y^2 - 3y = 0. 3. Combine similar terms: - This simplifies to 8 - 8y + 2y^2 + 2y - y^2 + y^2 - 3y = 0. 4. Further simplification: - This simplifies to 8 - 6y + 2y^2 = 0.

Now, we have the simplified equation 8 - 6y + 2y^2 = 0.

Solving for y

To solve for y, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a).

In our case, the coefficients are: - a = 2 - b = -6 - c = 8

Using the quadratic formula, we can calculate the solutions for y.

Calculating the Solutions

Applying the quadratic formula to our equation 8 - 6y + 2y^2 = 0, we get:

y = (-(-6) ± √((-6)^2 - 4*2*8)) / (2*2).

Solving this, we get: y = (6 ± √(36 - 64)) / 4, y = (6 ± √(-28)) / 4.

As the discriminant is negative, the solutions for y will involve complex numbers.

Final Result

The solutions for y are: - y = (6 + √(-28)) / 4 - y = (6 - √(-28)) / 4.

Therefore, the final result for the equation 2(2-y)^2 + (2-y)y + y^2 = 8 + y^2 - 3y = 0 involves complex numbers, specifically: - y = (6 + √(-28)) / 4 - y = (6 - √(-28)) / 4.