Consider the following statements: 1. If (a+b) is directly proportional to (a−b), then (a²+b²) is directly proportional to ab. 2. If a is directly proportional to b, then (a²−b²) is directly proportional to ab. Which of the statements given above is/are correct?
A.Both 1 and 2✓ Correct
B.1 only
C.Neither 1 nor 2
D.2 only
Explanation
Statement 1: a+b = k(a−b) means a/b is fixed, so a²+b² and ab are both proportional to b² — so proportional. Statement 2: a = kb makes a²−b² = (k²−1)b² and ab = kb², ratio constant — proportional. Both correct.
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