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Let x and y be the two numbers.
\n" ); document.write( "Given that certain number is 3 times another.
\n" ); document.write( "So, x = 3y ....(1)
\n" ); document.write( "Difference of their reciprocals is 8.
\n" ); document.write( "(1/x) - (1/y) = 8
\n" ); document.write( "Here LCM is xy. Multiply each fraction part with xy.
\n" ); document.write( "xy(1/x) - xy(1/y) = 8
\n" ); document.write( "(y - x)/xy = 8
\n" ); document.write( "Multiply both sides by xy
\n" ); document.write( "y - x = 8xy
\n" ); document.write( "From (1), we have x = 3y
\n" ); document.write( "y - (3y) = 8(3y)y
\n" ); document.write( "y - 3y = 8y x 3y
\n" ); document.write( "-2y = 24y^2
\n" ); document.write( "Add 2y to both sides of equation
\n" ); document.write( "-2y + 2y = 24y^2 + 2y
\n" ); document.write( "0 = 24y^2 + 2y
\n" ); document.write( "24y^2 + 2y = 0
\n" ); document.write( "take 2y common from the equation, we get
\n" ); document.write( "2y(12y + 1) = 0
\n" ); document.write( "Equate each part to zero
\n" ); document.write( "2y = 0 or 12y + 1 = 0
\n" ); document.write( "y = 0 or 12y = -1
\n" ); document.write( "y = 0 or y = -1/12
\n" ); document.write( "Therefore y is -1/12, 0.
\n" ); document.write( "But here y cannot be 0, because difference of reciprocals of two numbers is 8, then reciprocal of y is infinite which is not satisfying the condition.
\n" ); document.write( "so, y = -1/12.
\n" ); document.write( "when y = -1/12, then x = 3y = 3(-1/12)= -1/4
\n" ); document.write( "Therefore two numbers x and y are -1/4 and -1/12\r
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\n" ); document.write( "\n" ); document.write( "Regards,
\n" ); document.write( "Sudheer(edurite.com) \n" ); document.write( "