Question

The sum of two numbers is 8. Determine the numbers if the sum of their reciprocals is 8/5.

Answer 1

Hey!

Good Evening

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Let the two numbers be x and y

Then

=> x + y = 8 -----------(1)

=> x = 8 - y ----------------(2)

Also, given that sum of reciprocals

= > \frac{1}{x} + \frac{1}{y} = \frac{8}{15}

= > \frac{x + y}{xy} = \frac{8}{15}

Replacing (1) in above equation

= > \frac{8}{xy} = \frac{8}{15}

Cancelling 8 on Numerator sides and cross Multiplying

=> xy = 15

Using (2) in above equation

=> y(8 - y) = 15

=> y² - 8y + 15 = 0

By middle term splitting method

=> y² - 3y - 5y + 15 = 0

=> y(y - 3) - 5(y - 3) = 0

Thus

=> (y - 3)(y - 5) = 0

Thus y = 3 or y = 5

Using this in (2) we have

Thus x = 5 or x = 3

Thus the two numbers are 3 and 5

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Hope this helps ✌️

Good Night

Answer 2

Answer:

7.231662479 and 0.68337521 are the numbers. Finding answer was a difficult task. so please mark me as brainliest and follow me.

since 7.231662479+0.68337521=8

and 1/7.231662479+1/0.68337521=8/5

If You don't believe you can check it.