Answer:
Two required integers are 5 and 10.
Solution:
Given that a positive integer is twice another. The sum of the reciprocals of the positive integers is [tex]\frac{3}{10}[/tex]
We have to find the two integers.
Let assume that one integer = x
Since another integer is twice of first one, so second integer = 2x
Reciprocal of first integer = [tex]\frac{1}{x}[/tex]
Reciprocal of first integer = [tex]\frac{1}{2x}[/tex]
Given that sum of reciprocal = [tex]\frac{3}{10}[/tex]
[tex]\frac{1}{x}+\frac{1}{2 x}=\frac{3}{10}[/tex]
On solving above equation for x,
[tex]\frac{2+1}{2 x}=\frac{3}{10}[/tex]
[tex]\frac{3}{2 x}=\frac{3}{10}[/tex]
2x=10
x=5
First integer = x = 5
Second integer = 2x = 10
Hence two required integers are 5 and 10.
