Question
The difference between the squares of two consecutive natural numbers is equal to the sum of the two numbers.
Solution
(i) 92 - 82 = 81-64 = 17 = 9 + 8
102 - 92 = 100-81 = 19 = 10 + 9
152 - 142 = 225-196 = 29 = 15 + 14
1012 - 1002 = 10201-10000 = 201 = 101 + 100
(ii) If (n+1) and (n-1) are two consecutive even or odd natural numbers, then (n+1) x (n-1) = n2 -1
For example
10 x 12 = (11 - 1) x (11+1) = 112 - 1
11 x 13 = (12 - 1) x (12 + 1) = 122 -1
25 x 27 = (22 -1) x (26 - 1) x (26 + 1) = 262 - 1
