Question

The difference between the Square of the Two consecutive integers Is 408235 the sum of the number is

Answer 1

Given:

Difference between two integers = 408235

To Find:

Sum of the number

Solution:

Let the first number be =  x

Let the second number be = x+1

According to the question -

(x+1)² − x² = 408235  

Therefore,

x²+2x+1 − x² = 408235  

2x +1 = 408235  

2x = 408234

x = 204117

thus, first number = 204117

Second number = 204117 + 1 = 204118.

Answer: The sum of the numbers is = 408235

Answer 2

Given : The difference between the Square of the Two consecutive integers Is 408235

To find : sum of the number

Solution:

The difference between the Square of the Two consecutive integers  

= Sum of two numbers

difference between the Square of the Two consecutive integers  = 408235

Hence Sum of two numbers will be  = 408235

Here is proof

Let say two consecutive integers are

n  & n + 1

difference between the Square of the Two consecutive integers

= (n + 1)²  - n²

Apply  a² - b² = (a + b)(a - b)

a = n + 1

b = n

= ((n + 1)+n)((n + 1)- n)

= ((n + 1)+n)(1)

= (n + 1)+n

= Sum of two numbers

Hence  Sum of two numbers = 408235

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