The difference between two positive numbers is 6. If the sum of their squares is 180, then the sum of the numbers is

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The difference between two positive numbers is 6. If the sum of their squares is 180, then the sum of the numbers is

Asked on 2019-07-19 17:58:43 by Guest | Votes 0 | Views: 41 | Tags: algebra | quantitative aptitude | Add Bounty

The difference between two positive numbers is 6. If the sum of their squares is 180, then the sum of the numbers is
1). 81
2). 33
3). 18
4). 25

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Answered by Guest on 2019-07-19 18:00:52 | Votes 0 | #

Let the first positive number = x

Then the second positive number = y

We know that the difference between the two numbers is 6

⇒ x – y = 6

we know that the sum of their squares is 180

⇒ x² + y² = 180

we can use the identity

⇒ (x + y)²= x² + y² + 2xy

⇒ (x + y)²= 180 + 2xy

We need to know 2xy to find (x + y)²

To find 2xy we can use the identity

⇒ (x – y)²= x² + y² - 2xy

⇒ 6² = 180 - 2xy

⇒ 36 = 180 - 2xy

⇒ 2xy = 144

Now put 2xy = 144 in (x + y)²= 180 + 2xy

⇒ (x + y)² = 180 + 144

⇒ (x + y)² = 324

⇒ x + y = 18 (as both the numbers are positive hence their sum cannot be negative hence rejecting negative value of x + y)

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