Question

The difference between two positive integers is 5. If the sum of their squares is 1025, then the sum of the numbers is *​

Answer 1

Step-by-step explanation:

a - b = 5

a² + b² = 1025

a² - 2ab + b² = 25

a² + b² - 25 = 2ab

1025 - 25 = 2ab

2ab = 1000

(a+b)² = a²+b²+2ab

(a+b)² = 1025 + 1000

(a+b)² = 2025

a + b = 45

I hope it will help you

Answer 2

Given :  The difference between two positive integers is 5, sum of their squares is 1025

To find : sum of the numbers

Solution:

Let say two numbers are

N  & N + 5

as difference between two positive integers is 5

sum of their squares is 1025,

=> N² + (N + 5)² = 1025

=> N² + N² + 25 + 10N = 1025

=> 2N² + 10N - 1000 = 0

=> N² + 5N - 500 = 0

=> N² + 25N - 20N - 500 = 0

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

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

=> N = 20   , - 25 ( - 25 not possible as N can be +ve integer only )

Hence N = 20

sum of the numbers is N + N + 5

= 2N + 5

= 2(20) + 5

= 45

the sum of the numbers is 45

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