x + (x+1) + (x+2) ≥ 42
3x + 3 ≥ 42
3x ≥ 39
x ≥ 13
so the integers must be 13, 14, 15 or any other set of consecutive integers where the smallest is greater than 13 (such as 17, 18, 19 or 231, 232, 233)
Divide the sum of the three consecutive integers by 3: 138/3 = 46. The smallest of these integers will be one less than 46 and the largest will be one more than 46, so the three consecutive integers will be 45, 46, and 47.
Divide the sum of the three consecutive odd integers by 3: 402/3 = 134. The smallest of these integers will be two less than 134 and the largest will be two more than 134, so the three consecutive odd integers will be 132, 134, and 136.
Divide the sum of the three consecutive odd integers by 3: 51 / 3 = 17. The smallest of these integers will be two less than 17 and the largest will be two more than 17, so the three consecutive odd integers will be 15, 17, and 19.
Divide the sum of the three consecutive odd integers by 3: 225/3 = 75. The smallest of these integers will be two less than 75 and the largest will be two more than 75, so the three consecutive odd integers will be 73, 75, and 77.
Try squaring different integers (hint: in this case, the integers will be fairly small). If you find that the square of one integer is less than 27, and the square of the next integer is more than 27, you have your answer.
Divide the sum of the three consecutive integers by 3: 138/3 = 46. The smallest of these integers will be one less than 46 and the largest will be one more than 46, so the three consecutive integers will be 45, 46, and 47.
Divide the sum of the three consecutive odd integers by 3: -147 /3 = -49. The smallest of these integers will be two less than -49 and the largest will be two more than -49, so the three consecutive odd integers will be -47, -49, and -51.
Divide the sum of the three consecutive odd integers by 3: 402/3 = 134. The smallest of these integers will be two less than 134 and the largest will be two more than 134, so the three consecutive odd integers will be 132, 134, and 136.
The 3 consecutive odd positive integers are 7, 9 and 11.
Divide the sum of the three consecutive odd integers by 3: 51 / 3 = 17. The smallest of these integers will be two less than 17 and the largest will be two more than 17, so the three consecutive odd integers will be 15, 17, and 19.
Divide the sum of the three consecutive odd integers by 3: 159/3 = 53. The smallest of these integers will be two less than 53 and the largest will be two more than 53, so the three consecutive odd integers will be 51, 53, and 55.
Divide the sum of the three consecutive odd integers by 3: -3 /3 = -1. The smallest of these integers will be two less than -1 and the largest will be two more than -1, so the three consecutive odd integers will be -3, -1, and +1.
Divide the sum of the three consecutive odd integers by 3: -273 /3 = -91. The smallest of these integers will be two less than -91 and the largest will be two more than -91, so the three consecutive odd integers will be -89, -91, and -93.
Divide the sum of the three consecutive odd integers by 3: 183/3 = 61. The smallest of these integers will be two less than 61 and the largest will be two more than 61, so the three consecutive odd integers will be 59, 61, 63.
Divide the sum of the three consecutive odd integers by 3: 45/3 = 15. The smallest of these integers will be two less than 15 and the largest will be two more than 15, so the three consecutive odd integers will be 13, 15, and 17.
Divide the sum of the three consecutive odd integers by 3: 93 / 3 = 31. The smallest of these integers will be two less than 31 and the largest will be two more than 31, so the three consecutive odd integers will be 29, 31, and 33.
Divide the sum of the three consecutive odd integers by 3: 225/3 = 75. The smallest of these integers will be two less than 75 and the largest will be two more than 75, so the three consecutive odd integers will be 73, 75, and 77.