For what relation between a and b is the equation \sin \theta=\frac{a+b}{2\sqrt{ab}} possible?
- A. a=b ✓
- B. a \leq b
- C. a \geq b
- D. a \gt b
Correct Answer: A. a=b
Explanation
Since \sin \theta \leq 1, we have \frac{a+b}{2\sqrt{ab}} \leq 1, which simplifies to a+b \leq 2\sqrt{ab} or (\sqrt{a} - \sqrt{b})^2 \leq 0. Since a square cannot be negative, (\sqrt{a} - \sqrt{b})^2 = 0, implying a = b.
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