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The document shows the steps to solve an equation involving the squares of three odd integers separated by 2. It expands and combines terms to get x2 - 4x - 45 = 0, then factors this as (x - 9)(x + 5) = 0. The possible solutions are x = 9 or x = -5, but the question asks for the smallest number, which is 9.

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- 1. I will answer for 33. Because you had to give me the number to solve the exercise. If a different number you only have to replace the number. Every other number is an odd integer, so they are separated by 2: Let x be the first odd integer Let x+2 be the second odd integer Let x+4 be the third odd integer The square of the third is 33 less than the sum of the squares of the first two. x² + (x + 2)² - 33 = (x + 4)² Expand each one by using FOIL: x² + x² + 4x + 4 - 33 = x² + 8x + 16 Get everything on the left side: x² + x² + 4x + 4 - 33 - x² - 8x - 16 = 0 Combine like terms: (x² + x² - x²) + (4x - 8x) + (4 - 33 - 16) = 0 x² - 4x - 45 = 0 Factor that as: (x - 9)(x + 5) = 0 The zero product rule gives us two possible answers for the smallest number. x = 9 or x = -5 You already have 9, 11 and 13 Solution I will answer for 33. Because you had to give me the number to solve the exercise. If a different number you only have to replace the number.
- 2. Every other number is an odd integer, so they are separated by 2: Let x be the first odd integer Let x+2 be the second odd integer Let x+4 be the third odd integer The square of the third is 33 less than the sum of the squares of the first two. x² + (x + 2)² - 33 = (x + 4)² Expand each one by using FOIL: x² + x² + 4x + 4 - 33 = x² + 8x + 16 Get everything on the left side: x² + x² + 4x + 4 - 33 - x² - 8x - 16 = 0 Combine like terms: (x² + x² - x²) + (4x - 8x) + (4 - 33 - 16) = 0 x² - 4x - 45 = 0 Factor that as: (x - 9)(x + 5) = 0 The zero product rule gives us two possible answers for the smallest number. x = 9 or x = -5 You already have 9, 11 and 13