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The sum of squares of two positive numbers is greater than the twice of their product by 36. If the ratio of the numbers is 5 : 7, then find the numbers.
1. 10, 14
2. 15, 21
3. 20 : 28
4. 10, 13
5. 14, 10

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Correct Answer - Option 2 : 15, 21

Given:

Sum of squares - 2 × product = 36

Ratio = 5 : 7

Calculation:

Let the numbers be 5x and 7x

A.T.Q

(5x)2 + (7x)2 - 2× 5x × 7x = 36

⇒ 25x2 + 49x2 - 70x2 = 36

⇒ 4x2 = 36

⇒ x = 3

∴ The numbers are 15 and 21 

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