Q. 755.0( 1 Vote )

State whether the statements are true (T) or false (F).

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

Answer :

Let two consecutive numbers be x and (x + 1).

Then square of these numbers are x2 and (x + 1)2.

Difference of squares of these consecutive numbers = (x + 1)2 – x2

= x2 + 1 + 2x – x2 [, (a + b)2 = a2 + b2 + 2ab)

= 2x + 1

= x + x + 1

= (x) + (x + 1)

= sum of the two consecutive numbers x and x+1

Thus, difference of squares of two consecutive numbers = sum of the same consecutive numbers.

Hence, the statement is true.

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