Question

If two no. Are in ratio 2:5 and difference between the square of these no. Is 789 then find the numbers

Answer 1

Answer:

x = 2√(789/21)

y = √(19725/21)

Step-by-step explanation:

Let x and y be two numbers such that

        x : y = 2 : 5

⇒        x/y = 2/5

⇒           x = 2y/5

Then

According to second condition of question

      y² - x² = 789

Putting x = 2y/5 we get

      y² - (2y/5)² = 789

⇒    y² - 4y²/25 = 789

⇒    25y² - 4y² = 19725

⇒     25y² - 4y² = 19725

                 21y² = 19725

                     y² = 19725/21

                       y = √(19725/21)

Putting y = √(19725/21) in x = 2y/5 we get

   x = 2( √(19725/21) ) / 5 = 2√(19725/(21×25)) = 2√(789/21)

So

x = 2√(789/21)

y = √(19725/21)

Checking

x/y = 2√(789/21) /√(19725/21) = (2( √(19725/21) ) / 5) / √(19725/21) = 2 /5

y² - x² = (√(19725/21))² - (2√(789/21))² = 789