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Question 75

In the following question, state whether the statement is True (T) or False (F):

The difference of the squares of two consecutive numbers is their sum.


Solution

True
Let n and n + 1 be any two consecutive numbers, then their sum = n + n + 1 = 2n + 1
Now, the difference of their squares,
(n+1)2n2=n2+1+2nn2
=2n+1                               [(a+b)2=a2+2ab+b2] 

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