The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144, Find the positive difference between the squares of these two given numbers.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 540.
Let the numbers be x and y
(x - y)2 = 324
So, x - y = 18, xy = 144
(x + y)2 = (18)2 + 4 × 144 = 900
⇒ x + y = 30
Then, x is (30 + 18)/2 = 24 and y = 6
So, x2 - y2 = 242 - 62
⇒ 576 - 36 = 540