Advanced MathVery hardProduct from two squared sums
Advanced Math practice question
If (x + y)² = 49 and (x − y)² = 9, what is the value of xy?
Answer: 10
(x + y)² − (x − y)² = 4xy. So 49 − 9 = 40 = 4xy, and xy = 10.
Common wrong answers
- If you answered 20
- 20 halves 40 instead of dividing by 4; the difference of the two squares is 4xy.
- If you answered 29
- 29 is (49 + 9)/2 = x² + y², not xy.
- If you answered 40
- 40 is 4xy, one step short.
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