Question

the difference of two numbers is 5 and the difference of there reciprocal is 1/10 find the no

Answer 1

Let two numbers are a and b and let a > b

Now, a - b = 5 ...............(1)

and 1/b - 1/a = 1/10

=> (a - b)/ab = 1/10

=> 5/ab = 1/10

=> ab = 5*10

=> ab = 50

Now, (a + b)2 = (a - b)2 + 4*ab

=> (a + b)2 = 52 + 4*50

=> (a + b)2 = 25 + 200

=> (a + b)2 = 225

=> a + b = √(225)

=> a + b = √(15*15)

=> a + b = 15 ...........(2)

Add equation 1 and 2, we get

      2a = 15 + 5

=> 2a = 20

=> a = 20/2

=> a = 10

From equation 2, we get

     10 + b = 15

=> b = 15 - 10

=> b = 5

Therefore,two numbers are 10 and 5.

Answer 2

Answer:

Let two numbers are a and b and let a > b

Now, a - b = 5 ...............(1)

and 1/b - 1/a = 1/10

=> (a - b)/ab = 1/10

=> 5/ab = 1/10

=> ab = 5*10

=> ab = 50

Now, (a + b)2 = (a - b)2 + 4*ab

=> (a + b)2 = 52 + 4*50

=> (a + b)2 = 25 + 200

=> (a + b)2 = 225

=> a + b = √(225)

=> a + b = √(15*15)

=> a + b = 15 ...........(2)

Add equation 1 and 2, we get

     2a = 15 + 5

=> 2a = 20

=> a = 20/2

=> a = 10

From equation 2, we get

    10 + b = 15

=> b = 15 - 10

=> b = 5

Therefore,two numbers are 10 and 5.

Step-by-step explanation: