Question

The sum of a number x and its reciprocal is 8/15 less than thrice the sum of another number y and the reciprocal of y. If x = 3y, the value of x is
Between 8 and 12
Between 23 and 27
O
Between 33 and 37
O
Between 13 and 17​

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

Replacing (1) in above equation

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 ✌️