The sum of square of two numbers is 80 and the square of their difference is 16. What is the product of the two numbers?

The sum of square of two numbers is 80 and the square of their difference is 16. What is the product of the two numbers? Correct Answer 32

Let x and y be the two numbers. ATQ, x2 + y2 = 80.....(i) and (x - y)2 = 16 or, x2 - 2xy + y2 = 16 or, 80 - 2xy = 16 [ from (i) x2 + y2 = 80 ] or, 2xy = 80 - 16 = 64 or, xy = 32 so the product of the two number is 32
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