Question

Write each of the following numbers as difference of the square of two consecutive natural numbers. (i) 49 (ii) 75 (iii) 125 Write each of the following numbers as difference of the square of two consecutive natural numbers. (i) 49 (ii) 75 (iii) 125

Answer 1

Answer:

1) 49 = 2 × 24 + 1

49 = $25^{2}$ – $24^{2}$

2) 75 = 2 × 37 + 1

75 = $38^{2}$ – $37^{2}$

3) 125 = 2 × 62 + 1

125 = $63^{2}$ – $62^{2}$

Answer 2

i) 49 = 25² - 24²  

ii) 75 = 38² - 37²  

iii) 125 = 63² - 62²

Given:

(i) 49 (ii) 75 (iii) 125

To find:

Write each of the given numbers as difference of the square of two consecutive natural numbers.

Solution:

Let x be a natural number and the consecutive number is x+1

Difference of the square of two numbers

= (x + 1)²- x²

= x² + 1²+ 2x - x²

= 2x + 1 we will use this to solve above problem

i) Take 2x + 1 = 49

⇒ 2x = 48

⇒  x = 24

⇒ x + 1 = 24+1 = 25

The 2 consecutive numbers are 24 and 25

⇒ 49 = 25² - 24²  

(ii) Take 2x + 1 = 75  

⇒ 2x = 74

⇒ x = 37

⇒ x + 1 = 37+1 = 38

The 2 consecutive numbers are 37 and 38

⇒ 75 = 38² - 37²  

(iii) Take 2x +1 = 125

⇒ 2x = 124

⇒ x = 62

⇒ x+1 = 62+1 = 63

The 2 consecutive numbers are 62 and 63

⇒ 125 = 63² - 62²

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