3n² + 2 = 425 → 3n² = 423 → n² = 141 → n = √141 ≈ 11.874
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- But let's assume the sum is correct and solve numerically.
- Sum: (n−1)² + n² + (n+1)² = n²−2n+1 + n² + n²+2n+1 = 3n² + 2
- Set equal to 425:
- So smallest integer is n − 1 ≈ 10.874 → not integer — contradiction.
- But problem implies integer exists. Recheck: perhaps typo in setup?
- Wait — maybe three consecutive integers — let’s suppose the middle one is x. Then:
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