CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The difference of two natural numbers is 3 and the difference of their reciprocals is 328
 


Solution

Let one number be x and the other number be y.
According to question,
x-y=3 or x=y+3
Also,
1 over x minus 1 over y equals 3 over 28
Now putting the values of x in the above equation we get,
1 over y minus fraction numerator 1 over denominator 3 plus y end fraction equals 3 over 28 rightwards double arrow fraction numerator y plus 3 minus y over denominator y left parenthesis 3 plus y right parenthesis end fraction equals 3 over 28 rightwards double arrow 3 cross times 28 equals 3 y left parenthesis 3 plus y right parenthesis rightwards double arrow 28 equals y left parenthesis 3 plus y right parenthesis rightwards double arrow y squared plus 3 y minus 28 equals 0 rightwards double arrow y squared plus 7 y minus 4 y minus 28 equals 0 rightwards double arrow y left parenthesis y plus 7 right parenthesis minus 4 left parenthesis y plus 7 right parenthesis equals 0 rightwards double arrow left parenthesis y plus 7 right parenthesis left parenthesis y minus 4 right parenthesis equals 0 rightwards double arrow y equals negative 7 space o r space y equals 4
 We need to discard the value of y = -7 because y is a natural number. So the value of y = 4 
Therefore x = y+3=7
Hence the numbers are 4 and 7.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


Same exercise questions
View More


People also searched for
View More



footer-image