Question

The sum of two numbers is 9 and the sum of their reciprocals is ½. Find the numbers.

Answer 1

Heya!!!

Let the no.s be x and y

According to the question

x + y = 9 .... equation 1

and

1 / x + 1 / y = 1 / 2

2 ( x + y ) = xy .... equation 2

Now, put value of x + y in equation 2

2 ( 9 ) = xy

xy = 18

y = 18 / x

put value of y in equation 1

x + 18 / x = 9

x² + 18 = 9x

x² -9x + 18 = 0

x² - 6x - 3x + 18 = 0

x ( x - 6 ) -3 ( x - 6 ) = 0

x = 6 or x = 3

For x = 3 y = 6

For y = 6 x = 3

So, the no.s are 3. and 6

Have a nice time.