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If the product of two numbers is 60 and the sum of their squares is 169, then what is the sum of these two numbers?
1. 17
2. 15
3. 19
4. 13

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Correct Answer - Option 1 : 17

Given:

Product of two numbers = 60

Sum of the squares of the two numbers = 169

Formula used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

Let the two numbers be x and y

Then, according to the question:

xy = 60     ----eq.(1)

x2 + y2 = 169     ----eq.(2)

Also, (x + y)2 = x2 + y2 + 2xy

⇒ (x + y)2 = 169 + (2 × 60); From eq.1 and eq.2

⇒ (x + y)2 = 289

⇒ x + y = 17

∴ Sum of the two numbers = 17

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