The sum of two  numbers  is 15.if their reciprocal is 3/10.find two numbers .

Answer:

Let the two numbers are x and y

Therefore ATQ,

x+y=15 ---------------------1

If the sum of their reciprocals is 3/10.

then

1/x+1/y=3/10

x+y/xy=3/10

putting value from eq1.

15/xy=3/10

xy=50

x=50/y

Putting the value of x in eq1.

x+y=15

50/y+y=15

50+y^2=15y

y^2-15y-50=0

D=b^2-4ac

D=225-4*1*50.

D=25

x=-b+√D/2a

    -

x=15+5/2*1

x=20/2

x=10

 or 

x=15-5/2

x=5

Hence there are two numbers x=10 or 5 and y=5 or 10