Question

the sum of two numbers is 18 Determine the numbers if the sum of their reciprocals is 8/15

Answer 1

• Hey user !

let the number be x and y.

A/Q

=>x+ y = 18. . ......(..1)

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

Also, given that sum of reciprocals

=>1/x + 1/y = 8/15.

=>x+y/xy = 8.15

Replacing (1) in above equation

8/xy = 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 x = 5 or x = 3Thus the two numbers are 3 and 5

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