Question

the difference between two positive integers is 5 if the sum of their squares is 1025 then the sum of the number is

Answer 1

Given:-

• The difference between two positive integer is 5.
• If the sum of their square is 1025.

To find:-

• Find the sum of the number..?

Solutions:-

• Let one number be x and another number by y.

The difference between two positive integer is 5.

=> x - y = 5

=> x = 5 + y ......(i).

If the sum of their square is 1025.

=> x² + y² = 1025

Putting the value of x from Eq (i) in Eq (ii).

=> x² + y² = 1025

=> (5 + y)² + y² = 1025

=> 5² + y² + 10y + y² = 1025

=> 25 + 2y² + 10y = 1025

=> 2y² + 10y = 1025 - 25

=> 2y² + 10y = 1000

=> 2y² + 10y - 1000 = 0

=> 2(y² + 5y - 500) = 0

=> y² + 5y - 500 = 0

=> y² + 25y - 20y - 500 = 0

=> y(y + 25) - 20(y + 25) = 0

=> (y - 20) (y + 25) = 0

=> y = 20 or y = -25 (can't be in negative)

Putting the value of y in Eq (i).

=> x = 5 + y

=> x = 5 + 20

=> x = 25

So,

Sum of the integers

=> x + y

=> 25 + 20

=> 45

Hence, the sum of the integers is 45.