The difference of the squares of two consecutive numbers is their sum. Is the given statement true or false

Solution:

The statement ‘The difference of the squares of two consecutive numbers is their sum’ is true.

Let n and n+1 be the two consecutive numbers. Their sum = n+1 +n = 2n +1

(n+1)² - n² = n² + 2n+ 1² - n² = 2n +1

Thus proved.

✦ Try This: Is 100² - 99² = 199?

Let us consider two consecutive numbers 99 and 100.

Now, let us consider difference of the square of these two consecutive numbers,

Using standard identity : a² - b² = (a + b) (a - b)

Here, a = 100 and b = 99,

100² - 99² = (100 + 99) (100 - 99)

= (199) (1)

= 199

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 75

The difference of the squares of two consecutive numbers is their sum. Is the given statement true or false

Summary:

The statement ‘The difference of the squares of two consecutive numbers is their sum’ is true

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