Advanced MathVery hardProduct from a sum of squares and a difference
Advanced Math practice question
Two positive numbers have squares that add to 100, and the larger is 2 more than the smaller. What is the product of the two numbers?
Answer: 48
With smaller s: s² + (s + 2)² = 100 gives 2s² + 4s − 96 = 0, so s² + 2s − 48 = (s + 8)(s − 6) = 0 and the numbers are 6 and 8.
Common wrong answers
- If you answered 14
- 14 is their sum.
- If you answered 36
- 36 is the smaller number squared.
- If you answered 100
- 100 is the sum of the squares.
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