Question

Which values of x and y satisfy the equation 2x² + 4xy + 4y² - 2x + 1 = 0?

A) x = 1, y = 0
B) x = 0, y = 1
C) x = 0, y = 0
D) x = -1, y = -1

Answer 1

The values of x and y that satisfy the equation 2x² + 4xy + 4y² - 2x + 1 = 0 are x = -1/2 and y = 0, x = -1/2 and y = -1, x = 1 and y = 0, and x = 1 and y = -1.

Step-by-step explanation:

To find the values of x and y that satisfy the equation 2x² + 4xy + 4y² - 2x + 1 = 0, we need to factorize the equation and set it equal to zero. After factoring, we get (2x - 1)(x + 1) + 4y(y + 1) = 0. This means that either (2x - 1)(x + 1) = 0 or 4y(y + 1) = 0. Solving these two equations separately, we find that x = -1/2 or x = 1, and y = 0 or y = -1.

Therefore, the values of x and y that satisfy the equation are:

1. x = -1/2 and y = 0
2. x = -1/2 and y = -1
3. x = 1 and y = 0
4. x = 1 and y = -1