Question

The sum of the 2 numbers is 18 . The sum of their reciprocals 1/4 find the numbers?

Answer 1

Let the first number be x.
And the second number be 18 - x.
Then,
Their reciprocals will be = 1/x and 1/(18 - x) .

ATQ,

1/x + 1/(18 - x) = 1/4
(18 - x + x)/(18 - x)x = 1/4
(18×4) = (18 - x)x
72 = 18x - x²
x² - 18x + 72 = 0
x² - 12x - 6x - 72 = 0
x(x - 12) - 6(x - 12) = 0
(x - 6) (x - 12) = 0

Hence,
x = 6
x = 12

The numbers are 6 and 12.

Answer 2

Hi !


Let the first number be x.
Then , the  second number  will be 18 - x.


Their reciprocals will be = 1/x and 1/(18 - x) .


1/x + 1/(18 - x) = 1/4

(18 - x + x)/(18 - x)x = 1/4

(18×4) = (18 - x)x

72 = 18x - x²

x² - 18x + 72 = 0

splitting the middle term ,

x² - 12x - 6x - 72 = 0

x(x - 12) - 6(x - 12) = 0

(x - 6) (x - 12) = 0
x = 6 
x = 12

∴ The numbers are 6 and 12.