The sum of squares of two numbers is 80 and the square of difference between the two numbers is 36. Find the product of two numbers.
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Let the numbers are x and y,
Since, the sum of squares of two numbers is 80,
⇒ x² + y² = 80 -----(1)
And, the square of difference between the two numbers is 36,
⇒ (x - y)² = 36
⇒ x² + y² - 2 xy = 36
⇒ 80 - 2xy = 36 ( From equation (1) ),
⇒ -2xy = -44
⇒ xy = 22
Thus, the product of the two numbers is 22.
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