document.write( "Question 1119109: If log (x+y)/2 = 1/2 (log x + log y) prove that x = y \n" ); document.write( "
Algebra.Com's Answer #734566 by ikleyn(52776)\"\" \"About 
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document.write( "If log (x+y)/2 = 1/2 (log x + log y), then\r\n" );
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document.write( "\"%28x%2By%29%2F2\" = \"sqrt%28xy%29\"  ====>\r\n" );
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document.write( "x + y = \"2%2Asqrt%28xy%29\"    ====>  square both sides  ====>\r\n" );
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document.write( "\"x2+%2B+2xy+%2B+y%5E2\" = 4xy\r\n" );
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document.write( "\"x%5E2+-+2xy+%2B+y%5E2\" = 0  ====>\r\n" );
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document.write( "\"%28x-y%29%5E2\" = 0  ====>   x = y.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Proved ans solved.\r
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\n" ); document.write( "\n" ); document.write( "Notice:   The given condition is equivalent to \"%28x%2By%29%2F2\" = \"sqrt%28xy%29\",\r
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\n" ); document.write( "\n" ); document.write( "                and it is  VERY  WELL  KNOWN  FACT  that the last equality is equivalent to  x = y.\r
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\n" ); document.write( "\n" ); document.write( "                My solution gives you the proof of this fact.\r
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