If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is

Question

If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is

1. A. - 4
2. B. 0
3. C. 2 (Correct answer)
4. D. 4

Correct Answer

Option C — 2

Detailed Solution & Explanation

The correct answer is 2.

Key Points

• Rewrite: (x+2y)^2 + 2y^2 - 4y + 4 = (x+2y)^2 + 2(y-1)^2 + 2. Minimum when x+2y=0 and y=1: value = 0+0+2 = 2.