Advanced MathHardConsecutive integers from a sum of squares
Advanced Math practice question
The sum of the squares of two consecutive positive integers is 61. What is the larger of the two integers?
Answer: 6
Let the integers be n and n + 1: n² + (n + 1)² = 61, so 2n² + 2n + 1 = 61, n² + n − 30 = 0, (n + 6)(n − 5) = 0. Since n is positive, n = 5 and the larger integer is 6. Check: 25 + 36 = 61.
Common wrong answers
- If you answered 5
- 5 is the SMALLER integer; the question asks for the larger.
- If you answered 7
- 7 would pair with 6 to give 36 + 49 = 85, not 61.
- If you answered 30
- 30 is n² + n, or 61 − 31; not an integer in the pair.
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