Question
Mon November 14, 2011 By:
 

the difference of two numbers is 5 and the difference of their reciprocal is 1/10 .find the numbers.

Expert Reply
Mon November 14, 2011
Let the two numbers are a and b with a>b. 
 
This means that  
 
a-b = 5
 
and since a>b means 1/a<1/b
 
So, 1/b - 1/a = 1/10
 
Or, (a-b)/ab = 1/10
 
since a-b =5
 
means 5/ab = 1/10 means ab=50
 
Now. (a+b)2= (a-b)2 +4ab
 
hence 
 
(a+b)2= (5)2 +4×50
 
a+b = ±15
 
Let us take a+b=15 first
now a-b =5 adding these 2 eqns
2a=20 hence a=10, so b = 5
 
Now take a+b=-15
and a-b=5
 
add these 2 eqns to get 2a=-10 means a=-5 
hence b=-10
 
So the numbers are either 10 and 5
Or -5 and -10
 
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