The product of two numbers is 120 and the sum of their squares

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The product of two numbers is 120 and the sum of their squares is 289. The sum of the
two numbers is

1. 23
2. 7
3. 13
4. 169

Correct Option: A

Let the numbers be a and b.
According to the question,
ab = 120 ... (i)
and a² + b² = 289 ... (ii)
∴ (a + b)² = a² + b² +2ab
= 289 + 2 × 120
= 289 + 240 = 529
∴ a + b = √529 = 23