i would do trial and error; 7x9=63 11x11=121 difference of 58, which is too big, so try 3x5=15 7x7=49, difference of 34, again too big 1x3=3 5x5=25 difference of 22 answer=1,3,5
8,10,12
16, 17 and 18
the answer is 6
6 and 8. 6 * 8 = 48 6 * 6 = 36 48 - 36 = 12
Let the 3 consecutive number be represented by n, (n + 1) and (n + 2) Then, n(n + 1) + 37 = (n + 2)2 n2 + n + 37 = n2 + 4n + 4 3n = 33 n = 11 The three numbers are 11, 12 and 13.
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
Let the numbers be ;- n, n+1, n+2. Hence n(n+1) is 19 less than (n+2)^(2) It follows;- n(n+1)+ 19 = (n+2)^(2) Multiply out the brackets. n^(2) + n + 13 = n^(2) + 4n + 4 Collect 'like' terms. n^(2) - n&(2) + 4n - n = 13 - 4 Add 3n = 9 n = 3 n+ 1 = 4 n +2 = 5 Hence 3,4, & 5 are the consecutive numbers.
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