The square of the sum of two given natural numbers is 784, while the product of the two given numbers is 192. Find the positive difference between the squares of these two given numbers.
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. 112.
Given:
(x + y)2 = 784 and xy = 192
Now,
⇒ (x + y)2 = 784
⇒ (x + y) = 28
Squaring both sides
⇒ x2 + y2 + 2xy = 784
⇒ x2 + y2 + 2 × 192 = 784
⇒ x2 + y2 = 400
So,
x2 + y2 - 2xy = 400 - 2 × 192
x2 + y2 - 2xy = 16
⇒ (x - y)2 = 16
⇒ x - y = 4
Now,
⇒ x2 - y2 = (x + y) (x - y)
⇒ 28 × 4 = 112