Problem

3. Find three consecutive integers such that the sum of the squares of the first 2 is $=12+$ more than the square of the third.

Answer

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Answer

Check if they satisfy the given condition: \((-3, -2, -1)\) does, so the final answer is \(\boxed{-3, -2, -1}\)

Steps

Step 1 ：Let the three consecutive integers be x, x+1, and x+2.

Step 2 ：Write the equation: \(x^2 + (x+1)^2 = (x+2)^2 + 12\)

Step 3 ：Solve the equation to find the value of x: \(x = -3, 5\)

Step 4 ：Find the corresponding consecutive integers for both cases: \((-3, -2, -1)\) and \((5, 6, 7)\)

Step 5 ：Check if they satisfy the given condition: \((-3, -2, -1)\) does, so the final answer is \(\boxed{-3, -2, -1}\)

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