document.write( "Question 1144142: show that for any integers x and y :2xy<= x^2 +y^2
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Algebra.Com's Answer #765147 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Start from the inequality\r\n" );
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document.write( "     >= 0,\r\n" );
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document.write( "which is valid for all real numbers \"x\" and \"y\".\r\n" );
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document.write( "It is equivalent to\r\n" );
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document.write( "     >= 0.\r\n" );
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document.write( "Add  2xy to both sides.  You will get an equivalent inequality\r\n" );
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document.write( "     >= 2xy.\r\n" );
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document.write( "It is EXACTLY what has to be proved.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and completed.\r
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\n" ); document.write( "\n" ); document.write( "It is one of the classic and basic inequalities in Elementary Math, but the problem's formulation is NOT ADEQUATE.\r
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\n" ); document.write( "\n" ); document.write( "The adequate formulation is THIS :\r
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document.write( "    show that for any real numbers x and y   2xy <= x^2 +y^2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "with replacing \"any integers x and y\" by \"any real numbers x and y\".\r
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\n" ); document.write( "\n" ); document.write( "Actually, this replacement is VERY important and shows that the person who invented/created the original post, \r
\n" ); document.write( "\n" ); document.write( "is UNPROFESSIONAL in Math.\r
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