# The sum of two numbers is 16 and the sum of their reciprocals is 1/3 .Find the numbers.

2
by dweejareddy

2014-10-05T11:59:51+05:30

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Two numbers are : x and y
Sum is 16
⇒x+y = 16
⇒x = 16-y
Sum of reciprocals = 1/3

⇒16×3 = 16y - y²

⇒ y² - 16y + 48 = 0

⇒ y² - 12y - 4y + 48 = 0

⇒ (y-12)(y-4) = 0

⇒ y=4 or 12

⇒x=12 or 4

So numbers are 4,12

• Brainly User
2014-10-05T12:04:02+05:30
Let the two numbers be x and y
ATQ;
x+y=16 .................................................(i)
x=16-y...................................................(ii)
and
+=1/3
(taking LCM)
->()=1/3
from (i)
->=1/3
->xy=48
from (ii)
->(16-y)y=48
->16y-=48
->-16y+48=0
->-12y-4y+48=0
->y(y-12)-4(y-12)=0
->y=12,4
Hence the value of x and y is 12 and 4