The required two integers are 7 and 14
This is a question on word problems leading to the simultaneous equation:
Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1
Also, if the sum of the reciprocals of the two positive integers is 3/14, then:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2
Substitute equation 1 into 2
[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]
Find the LCM of 2y and y
[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]
Substitute y = 7 into equation 1:
Recall that x = 2y
[tex]x = 2(7)\\x = 14[/tex]
Hence the required two integers are 7 and 14.
Learn more here: https://brainly.com/question/17671977
