Question

the difference of the squares of two consecutive even numbers is 44 . find the numbers .

Answer 1

let two conescutive even numbers be x and x+2.
so,  (x+2)²-x²=44
x²+4x+4-x²=44
4x+4=44
4x=40
x=10.
so, numbers are 10 and 12

Answer 2

Given : The difference of the squares of two consecutive even numbers is 44

To find : The said numbers.

Solution :

The numbers are 10 and 12

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to find the said numbers by using given conditions)

Let, first even number = x

So, second even number = (x+2) [As, they are consecutive even numbers]

Square of first even number = x²

Square of second even number = (x+2)² = (x²+4x+4)

According to the data mentioned in the question,

x²+4x+4-x² = 44

4x+4 = 44

4 (x+1) = 4 × 11

(x+1) = 11

x = 11-1

x = 10

So, first even number = x = 10

Second even number will be = x+2 = 10+2 = 12

Hence, the two numbers are 10 and 12