document.write( "Question 844224: if a,b,c are in HP and ab + bc + ca = 15 then ca =
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Algebra.Com's Answer #508728 by Edwin McCravy(20056) $\"\"$ $\"About$

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if a,b,c are in HP and ab + bc + ca = 15 then ca =
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document.write( "Since a,b,c are in harmonic progression, their \r\n" );
document.write( "reciprocals ,, form an arithmetic sequence:\r\n" );
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document.write( "Let d be the common difference.  Then\r\n" );
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document.write( "Solve each for d\r\n" );
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document.write( "Since both equal d, they are equal to each other:\r\n" );
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document.write( "Multiply through by LCD of abc\r\n" );
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document.write( "ac - bc = ab - ac\r\n" );
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document.write( "2ac = ab + bc\r\n" );
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document.write( "And since we are given that\r\n" );
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document.write( "ab + bc + ca = 15\r\n" );
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document.write( "We can substitute 2ac for ab + bc and get\r\n" );
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document.write( "2ac + ca = 15\r\n" );
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document.write( "And since ac is the same as ca\r\n" );
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document.write( "2ca + ca = 15\r\n" );
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document.write( "3ca = 15\r\n" );
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document.write( "ca = 5\r\n" );
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document.write( "Edwin

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