The sum of the two numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers.

x+y=15

y+x/xy=3/10

1/x + 1/15-x=3/10

150=45x-3x2

3x2-45x-150=0

x2-15-50=0

Therefore no.are 5 and 10

let the numbers be x and y

so

x+y = 15 -------------------------(i)

and 1/x + 1/y = 3/10

==> (y + x)/xy = 3/10 (putting (i))

15/ xy = 3/10

5/xy = 1/10

xy = 50 --------------------(ii)

x = 50/y -----------------------(iii)

50/y + y = 15

50 + y² = 15y

y² - 15y + 50 = 0

(y-10)(y-5) = 0

y = 10 and y = 5

now there will be 2 numbers for 'x'

substituting y as 10 we get

x = 5 ;

substituting y as 5 we get

x = 10;

so the numbers are x = 10 and y = 5 and viceversa !

PLEASE APPROVE !

let the numbers be x & y.

x+y=15............1

1/x + 1/y = 3/10...........2

y+x /xy = 3.10

10(x+y)= 3xy.

10(15)= 3(15-y)y.

50 = 15y-y².

y²-15y+50 = 0.

y²-10y-5y+50 = 0.

y(y-10)-5(y-10)=0.

(y-5)(y-10)=0.

y = 5 or 10.

Similarly x = 10 or 5.

The numbers are 5 and 10.