Advanced MathVery hardProduct from a sum and a difference
Advanced Math practice question
For numbers x and y, x + y = 9 and x − y = 5. Using the identity (x + y)² − (x − y)² = 4xy, what is the value of xy?
Answer: 14
(x + y)² − (x − y)² = 81 − 25 = 56 = 4xy, so xy = 14.
Common wrong answers
- If you answered 7
- 7 is x itself (x = 7, y = 2); the product is 14.
- If you answered 28
- Divide 56 by 4, not by 2.
- If you answered 56
- 56 is 4xy; divide by 4.
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