Question

Find two consecutive numbers such that the difference of their squares is 45

Answer 1

let the two numbers be x and x+1

according to the question:

(x+1)^2 - x^2 = 45

x^2+1+2x - x^2 = 45

2x + 1 = 45

2x= 44

x = 22

the other number is x+1 = 22+1 = 23

therefore, the two consecutive numbers are 22 and 23

Hope it helped u....

Answer 2

The two consecutive numbers are 22 and 23

Given : The difference of the squares of the two consecutive numbers is 45

To find : The two consecutive numbers.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to determine the two consecutive numbers)

Let, first number = x

As, the two numbers are consecutive.

So, the second number = (first number +1) = (x+1)

(Difference between two consecutive whole numbers is always equal to 1.)

Square of first number = (x)² = x²

Square of second number = (x+1)² = (x²+2x+1)

The difference of their squares :

= (x²+2x+1) - (x²)

= x²+2x+1-x²

= 2x+1

According to the data mentioned in the question,

2x+1 = 45

2x = 45-1

2x = 44

x = 44/2

x = 22

First number = x = 22

Its consecutive number = x+1 = 22+1 = 23

(These will be considered as the final results.)

Hence, the two consecutive numbers are 22 and 23