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The difference between two numbers is 5 and the sum of their squares is 125. What could be the product of the numbers? Also explain the steps. Meaningless and useless answer will be deleted and pints will be lost.

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Answer:

Given :

  • The difference between two numbers is 5.
  • The sum of their squares is 125.

To find :

  • Product of the numbers?

Solution :

☯ Let two numbers be x and y.

★ According to the Question:

  • The difference between two numbers is 5.

⇒ x - y = 5⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ❬ eq (1) ❭

Also,

  • The sum of their squares is 125.

⇒ x² + y² = 125 ⠀⠀⠀⠀⠀⠀⠀❬ eq (2) ❭

⠀━━━━━━━━━━━━━━━━━━━━━

As we know that,

★ (x - y)² = x² + y² - 2xy

Now from eq (1) and eq (2),

⇒ (5)² = 125 - 2xy

⇒ 25 = 125 - 2xy

⇒2xy = 125 - 25

⇒ 2xy = 100

⇒ xy = 100/2

⇒ xy = 50

∴ Hence, Product of the numbers is 50.

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