document.write( "Question 1019866: Which is the greatest/largest number x so that
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Algebra.Com's Answer #635890 by ikleyn(53763) $\"\"$ $\"About$

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document.write( "I think this problem should/must be reformulated in this way:\r\n" );
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document.write( "  Find the greatest/largest number x so that \r\n" );
document.write( "      (1)\r\n" );
document.write( "  for all real positive a, b and c.\r\n" );
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document.write( "Solution\r\n" );
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document.write( "By completing the square you get\r\n" );
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document.write( " = .\r\n" );
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document.write( "So   is always >= 3a for positive a, and the equality is achieved at a=1.\r\n" );
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document.write( "Similarly,   is always >= 3b  for positive b, and the equality is achieved at b=1;\r\n" );
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document.write( "             is always >= 3c for positive c, and the equality is achieved at c=1.\r\n" );
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document.write( "Therefore, x=13*3*3 = 27 in (1) provides that (1) is always true, and you can not use greater x.\r\n" );
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document.write( "Thus the answer is: x=27.\r\n" );
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