document.write( "Question 1060963: The sum of a number and its reciprocal is 89/40. find the number \n" ); document.write( "
Algebra.Com's Answer #675792 by rothauserc(4718)\"\" \"About 
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let x be the number, then
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\n" ); document.write( "x + 1/x = 89/40
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\n" ); document.write( "(x^2 +1) / x = 89/40
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\n" ); document.write( "cross multiply the fractions
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\n" ); document.write( "40(x^2 +1) = 89x
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\n" ); document.write( "40x^2 -89x +40 = 0
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\n" ); document.write( "use quadratic formula
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\n" ); document.write( "x = (-(-89) + square root( (-89)^2 -4*40*40) ) / (2*40) = 1.6 = 8/5
\n" ); document.write( "x = (-(-89) - square root( (-89)^2 -4*40*40) ) / (2*40) = 0.625 = 5/8
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\n" ); document.write( "There are two solutions
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\n" ); document.write( "x = 8/5, x = 5/8
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\n" ); document.write( "check the solutions
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\n" ); document.write( "x = 1.6 = 16/10 = 8/5
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\n" ); document.write( "8/5 + 5/8 = 64/40 + 25/40 = 89/40, answer checks
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\n" ); document.write( "625/1000 = 25/40 = 5/8
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\n" ); document.write( "5/8 + 8/5 = 25/40 + 64/40 = 89/40, answer checks \n" ); document.write( "
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