document.write( "Question 253945: The sum of the reciprocals of two consecutive odd integers is 20/99. Find the two integers. \n" ); document.write( "

Algebra.Com's Answer #186337 by palanisamy(496) $\"\"$ $\"About$

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Let the two consecutive odd integers be x and x+2.
\n" ); document.write( "Given, (1/x)+(1/x+2) = 20/99
\n" ); document.write( " (x+2+x)/x(x+2) = 20/99
\n" ); document.write( " 99(2x+2) = 20x(x+2)
\n" ); document.write( " 198x+198 = 20x^2+40x
\n" ); document.write( " 20x^2+40x-198x-198 = 0
\n" ); document.write( " 20x^2-158x-198 = 0
\n" ); document.write( " 10x^2 - 79x-99 = 0
\n" ); document.write( " 10x^2-90x+11x-99 = 0
\n" ); document.write( " 10x(x-9)+11(x-9)=0
\n" ); document.write( " (x-9)(10x+11) =0
\n" ); document.write( " x-9 = 0 or 10x+11 = 0
\n" ); document.write( " x = 9 or 10x = -11
\n" ); document.write( " x = 9 or x = - 11/10
\n" ); document.write( "Since x cannot be a fraction, take x = 9.
\n" ); document.write( " So the given numbers are 9 and 11 \n" ); document.write( "

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