document.write( "Question 1208897: For 0 < a < b, let h be defined by\r
\n" ); document.write( "\n" ); document.write( "1/h = (1/2)[(1/a) + (1/b)].\r
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\n" ); document.write( "\n" ); document.write( "Note: The number h is called the harmonic mean of a and b.\r
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Algebra.Com's Answer #847414 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"1%2Fh\"\"%22%22=%22%22\"\"expr%281%2F2%29%281%2Fa%2B1%2Fb%29\"\r\n" );
document.write( "\"1%2Fh\"\"%22%22=%22%22\"\"expr%281%2F2%29%28%28b%2Ba%29%2F%28ab%29%29\"\r\n" );
document.write( "\"1%2Fh\"\"%22%22=%22%22\"\"%28a%2Bb%29%2F%282ab%29\"\r\n" );
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document.write( "\"0%3Ca%3Cb\"\r\n" );
document.write( "add a to all three parts\r\n" );
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document.write( "\"a%3C2a%3Ca%2Bb\"\r\n" );
document.write( "divide all three parts by 2ab\r\n" );
document.write( "\"a%2F%282ab%29%3C%282a%29%2F%282ab%29%3C%28a%2Bb%29%2F%282ab%29\"\r\n" );
document.write( "\"1%2F%282b%29%3C1%2Fb%3C%28a%2Bb%29%2F%282ab%29\"\r\n" );
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document.write( "\"0%3Ca%3Cb\"\r\n" );
document.write( "add b to all three parts\r\n" );
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document.write( "\"b%3Ca%2Bb%3C2b\"\r\n" );
document.write( "divide all three parts by 2ab\r\n" );
document.write( "\"b%2F%282ab%29%3C%28a%2Bb%29%2F%282ab%29%3C%282b%29%2F%282ab%29\"\r\n" );
document.write( "\"1%2F%282a%29%3C%28a%2Bb%29%2F%282ab%29%3C1%2Fa\"\r\n" );
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document.write( "Put these two together:\r\n" );
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document.write( "\"1%2F%282b%29%3C1%2Fb%3C%28a%2Bb%29%2F%282ab%29\" and \"1%2F%282a%29%3C%28a%2Bb%29%2F%282ab%29%3C1%2Fa\"\r\n" );
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document.write( "Ignoring the first parts of each:\r\n" );
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document.write( "\"1%2Fb%3C%28a%2Bb%29%2F%282ab%29%3C1%2Fa\"\r\n" );
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document.write( "We use the fact that if \"0%3Cx%3Cy%3Cz\" then \"matrix%281%2C2%2C0%3C1%2Fz%3C1%2Fy%3C1%2Fx%2C%22%22%29\"\r\n" );
document.write( "I'll prove that if you need it.  But I'll use it here\r\n" );
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document.write( "So that applies above and we have\r\n" );
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document.write( "\"a%3C%282ab%29%2F%28a%2Bb%29%3Cb\"\r\n" );
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document.write( "And since at the top we showed \"1%2Fh\"\"%22%22=%22%22\"\"%28a%2Bb%29%2F%282ab%29\"\r\n" );
document.write( "then \"h=%282ab%29%2F%28a%2Bb%29\"\r\n" );
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document.write( "So \"a%3Ch%3Cb\" \r\n" );
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document.write( "Edwin
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