document.write( "Question 789858: the sum of the reciprocals of two consecutive even integers is 9/40. what are the integers? \n" ); document.write( "

Algebra.Com's Answer #478962 by mananth(16946) $\"\"$ $\"About$

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let the integers be x & x+2\r
\n" ); document.write( "\n" ); document.write( "1/x + 1/(x+2) =9/40\r
\n" ); document.write( "\n" ); document.write( "multiply equation by 40x(x+2)\r
\n" ); document.write( "\n" ); document.write( "40(x+2)+40x=9x(x+2)\r
\n" ); document.write( "\n" ); document.write( "40x+80+40x=9x^2+18x\r
\n" ); document.write( "\n" ); document.write( "9x^2+18x-80x-80=0\r
\n" ); document.write( "\n" ); document.write( "9x^2-62x-80=0\r
\n" ); document.write( "\n" ); document.write( "solve by quadratic formula\r
\n" ); document.write( "\n" ); document.write( "a= 9 , b= -62 , c= -80
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\n" ); document.write( "b^2-4ac= 3844 + 2880
\n" ); document.write( "b^2-4ac= 6724
\n" ); document.write( " $\"%09sqrt%28%096724%09%29=%0982%09\"$
\n" ); document.write( " $\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( " $\"x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( "x1=( 62 + 82 )/ 18
\n" ); document.write( "x1= 8.00
\n" ); document.write( " $\"x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( "x2=( 62 -82 ) / 18
\n" ); document.write( "x2= -1.11 \r
\n" ); document.write( "\n" ); document.write( "8 is an integer\r
\n" ); document.write( "\n" ); document.write( "so the integers are 8 & 10\r
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