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

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

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 .

16
32
58
104

Correct Answer: 16

Explanation:

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 .

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