Consider a question and two statements:<br>Question: Is a^2+b^2+c^2-ab-bc-ca (a, b, c are distinct real numbers) <strong>ALWAYS</strong> positive?<br>Statement-I: a \gt b \gt c<br>Statement-II: a+b+c=0<br>Which one of the following is correct in respect of the question and the statements?
- A. Statement-I alone is required to answer the question
- B. Statement-II alone is required to answer the question
- C. Both Statement-I and Statement-II are required to answer the question
- D. Neither Statement-I nor Statement-II is required to answer the question ✓
Correct Answer: D. Neither Statement-I nor Statement-II is required to answer the question
Explanation
The expression a^2+b^2+c^2-ab-bc-ca can be rewritten as \frac{1}{2}[(a-b)^2+(b-c)^2+(c-a)^2]. For any distinct real numbers, the sum of these squares is strictly positive. Therefore, it is always positive, and neither statement is required to answer the question.
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