Question

sum of two numbers is 27. The sum of their reciprocals is 3 by 20 find the numbers.

Answer 1

let the two number be x and y.
ATQ, x + y =27...........(1)
1/x + 1/ y =3/20.......(2)
from equation 1 ,we have,
x=27-y.........(3)
put the value of x in equation 2 ,to get,
$\frac{1}{27 - y} + \frac{1}{y} = \frac{3}{20}$
${y}^{2} - 27y + 180 = 0$
now,
$d = {b}^{2} - 4ac$
$d = {( - 27)}^{2} - 4(1)(180)$
$d = 9$
then,
$y = ( - b + - \sqrt{d } ) \div 2a$
$y = \frac{ -( - 27) + - \sqrt{9} }{2(1)}$
$y = 15 \: or \: y = 12$
similarly,
if y=15 ,then x=12
but if, y=12, then x=15

Answer 2

Answer:

let two natural no' s are x and y

Step-by-step explanation:

According to question ,

x+ y =27- (1) eq

1/x-1/y =3/20 -(2) eq

from eq (1)

x=27 -y -(3)

put the value of x in eq (2)

1/27-y +1/y=3/20

y^2-27 y + 180 =0

Now

d= b^2 -4 ac