Question

14. The sum to numbers is 8 and the sum of their reciprocals is 1 Find the numbers.
15. In figure ZBED = ZBDE and E divides BC in ratio 2:1. Prove that AF BE = 2AD CF.

plzz solve fast​

Answer 1

Answer:

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}=>

x

1

+

y

1

=

15

8

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

xy

x+y

=

15

8

Replacing (1) in above equation

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

xy

8

=

15

8

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