InterviewSolution
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InterviewSolution
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The difference of two numbers is 4.If the difference of their reciprocals is 4/21, find the numbers |
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Answer» Let the larger number be x and the smaller number be y . Then , ` x- y = 4 " "`… (i) And , ` (1)/( y) - (1)/(x) = ( 4)/( 21)" " [ because x gt y rArr (1)/( y) gt (1)/(x)]` `rArr (x - y )/( xy ) = ( 4)/( 21)` ` rArr ( 4) /( xy ) = ( 4)/( 21) rArr xy = 21 " "`[using (i)] ` therefore ( x+ y ) = sqrt ((x- y ) ^(2) + 4xy) ` ` " " = sqrt( 4^(2) + 4 xx 21 ) = sqrt ( 16 + 84 ) = sqrt (100) = pm 10 ` Thus, we have `{:(x- y = 4,,... (i)),(x+y= 10,,... (ii)):}} or {{:(x- y = 4,,... (iii)),(x+y = - 10,, ... (iv)):}` On solving (i) and (ii), we get x = 7 and y = - 3 On solving (iii) and (iv), we get x = - 3 and y = - 7. Hence, the required numbers are ( 7 and 3) or (-3 and - 7). |
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