The sum of two numbers is 28 and the sum of their squares is 528. Find the square root of the product of both the numbers.
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Correct answer: D
Explanation
The correct answer is Option 4 i.e 8√2.
The sum of two numbers is 28 and the sum of their squares is 528.
⇒ x + y = 28
⇒ x = (28 - y) ....(1
⇒ x2 + y2 = 528 ...(2
⇒ (x + y)2 = x2 + y2 + 2xy
⇒ 282 = 528 + 2xy
⇒ 784 - 528 = 2xy
⇒ 256/2 = xy
⇒ xy = 128
The square root of the product of both the numbers = √xy = √128 = 8√2