Question:
If \(x - 2y = 4\), then the minimum value of \(xy\) is
If \(x - 2y = 4\), then the minimum value of \(xy\) is
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For a quadratic expression \(ay^2 + by + c\) with \(a > 0\), minimum occurs at vertex \(y = -\frac{b}{2a}\).
Updated On: Apr 16, 2026
- \(-2\)
- 0
- 1
- \(-3\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Express \(x\) in terms of \(y\) and form a quadratic.
Step 2: Detailed Explanation:
\(x = 2y + 4\).
Let \(P = xy = y(2y + 4) = 2y^2 + 4y = 2(y^2 + 2y) = 2[(y+1)^2 - 1] = 2(y+1)^2 - 2\).
Minimum occurs when \((y+1)^2 = 0\), i.e., \(y = -1\), \(x = 2\).
Minimum value = \(-2\).
Step 3: Final Answer:
Option (A) \(-2\).
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