The sum of squares of two numbers is 68 and the squares

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The sum of squares of two numbers is 68 and the squares of their difference is 36. The product of the two number is ?

1. 16
2. 32
3. 58
4. 104

Correct Option: A

Let the number be a and b .
Then a² + b² = 68 ....(i)
and (a - b)² = 36
Now, (a - b)² = 36 ....(ii)
⇒ a² + b² - 2ab = 36
⇒ 68 - 2ab = 36
⇒ 2ab = 32
⇒ ab = 16 .