Question:
Difference of two numbers is 5. Difference of their reciprocals is 1/10.find the numbers.
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
So, the numbers are 10 and 5
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