What are the two natural numbers whose product is 2400 and the sum of whose squares is 5200?
Detailed Explanation:
Let the two numbers be A and B. Given AB = 2400 and A² + B² = 5200.
Using identity (A + B)² = A² + B² + 2AB: (A + B)² = 5200 + 2(2400) = 5200 + 4800 = 10000. Therefore, A + B = 100.
Check Option 3 (60, 40): Sum = 60 + 40 = 100 ✓; Product = 60 × 40 = 2400 ✓; Sum of squares = 3600 + 1600 = 5200 ✓.
Therefore, the numbers are 60 and 40, making Option 3 the correct answer.
Question 4 of 8 Number System
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