Call the numbers: x, (x+1), (x+2) Product of the smaller two: x(x+1) = x2 + x Square of the largest number: (x+2)2 = x2 + 4x + 4 Product of the smaller two is 40 less than the largest one squared: (x2 + x) = (x2 + 4x + 4) - 40 x2 + x = x2 + 4x - 36 0 = 3x - 36 0 = x - 12 x = 12 x+1 = 13 x+2 = 14 Check: Product of the smaller two = (12)(13) = 156 Square of the largest = 196. 156 is in fact 40 less than 196.
5, 6 and 7
8, 9, and 10
12, 13 and 14
14, 15, 16
8, 10, 12
Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number.
5,6,7
11,12,13
8,10,12
5, 6 and 7
8, 9, and 10
16, 17 and 18
12, 13 and 14
1, 3, 5
14, 15, 16
4, 6, and 8
8, 10, 12