Question

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

(PLEASE GIVE THE EXPLANATION.)

Answer 1

i)24 and 25 ii)37 and 38 iii)62 and 63

Let one Natural number be x

Another natural number=x+1

i)Difference of their squares=49

(x+1)²-x²=49

(a+b)^2 = a^2 +2ab+b^2

x²+2x+1-x²=49

2x=48

x=24

Two consecutive Numbers are 24 and 25.

ii)Difference of their squares =75

(x+1)²-x²=75

x²+2x+1-x²=75

2x=74

x=37

The consecutive numbers are 37 and 38

iii)Difference of their squares =125

(x+1)²-x²=125

x²+2x+1-x²=125

2x=124

x=62

The consecutive numbers are 62 and 63