Is it true that the difference of the squares of two consecutive numbers is their sum?

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True

False

answer is A.

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Detailed Solution

Given statement, the difference of the squares of two consecutive numbers is their sum.
Assume that two consecutive integers are n and n+1.
Find difference of squares of (n + 1) and n by using identity

x + y x − y = x 2 − y 2

(n + 1) 2 − n 2 = (n + 1 + n) (n + 1 − n) ⇒ (n + 1) 2 − n 2 = (n + 1 + n) (1) ⇒ (n + 1) 2 − n 2 = (n + 1 + n) ⇒ (n + 1) 2 − n 2 = (n + 1) + n

Note that difference of the squares of two consecutive numbers can be written as sum of those numbers hence conclude that given statement is true.
Hence, option 1 is correct.

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