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CBSE Class 10 Answered

The difference of two natural numbers is 3 & the difference of their reciprocals is 3/28.Find the numbers.
Asked by agraharianiruddha | 25 Jul, 2018, 09:15: PM
answered-by-expert Expert Answer
According to the question,
Let x and y be the numbers and 
x - y = 3 
x - 3 = y begin mathsize 16px style 1 over straight x minus 1 over straight y equals 3 over 28
rightwards double arrow fraction numerator begin display style 1 end style over denominator begin display style straight x end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style straight x space minus space 3 end style end fraction equals fraction numerator begin display style 3 end style over denominator begin display style 28 end style end fraction
rightwards double arrow fraction numerator straight x minus 3 minus straight x over denominator straight x squared minus 3 straight x end fraction equals fraction numerator begin display style 3 end style over denominator begin display style 28 end style end fraction
rightwards double arrow 3 straight x squared minus 9 straight x equals negative 84
rightwards double arrow 3 straight x squared minus 9 straight x plus 84 equals 0
rightwards double arrow straight x squared minus 3 straight x plus 28 equals 0
rightwards double arrow left parenthesis straight x space minus space 7 right parenthesis left parenthesis straight x space plus space 4 right parenthesis equals 0
rightwards double arrow straight x space equals space 7 space or space straight x space equals space minus 4
rightwards double arrow straight y equals 7 minus 3 equals 4 space and space straight y space equals negative 4 space minus 3 space equals space minus 7 end style
Answered by Sneha shidid | 26 Jul, 2018, 09:08: AM
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