Question

The sum of two numbers is 25.The sum of their reciprocal is 1/4.Find the numbers.

Answer 1

Answer:

x=20 y= 5

Step-by-step explanation:

x+y=25

1/x +1/y=1/4

(x+y)/xy=1/4

4(x+y)=xy

as x+y=25

4(25)=xy

x=100/y

100/y + y = 25

y^2 - 25y + 100=0

y^2 -20y - 5y +100= 0

(y-5)(y-20)=0

x=20 y= 5

Answer 2

Answer:

The final answer is ( x , y ) = ( 20 , 5) , ( 5 , 20 )

Step-by-step explanation:

Given,

Sum of two numbers = 25

Sum of reciprocal of two numbers = 1/4

Let the two numbers be x,y

x + y =25   (1)

1/x + 1/y = 1/4  (2)

y = 25 - x  (3)

Changing (2) we get,

( x + y ) / xy = 1/4

25 / xy = 1/4

xy =100

Applying (3) in the above equation we get,

x(25-x) = 100

$x^2 - 25x + 100 = 0$

By factorizing we get x = 20 , x =5

Hence, There are two sets of answers

( x , y ) = ( 20 , 5) , ( 5 , 20 )

How to factorize

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