document.write( "Question 1209896: Let x and y be real numbers. Find the maximum value of (x + y)^2, if x and y satisfy x^2 + y^2 = 5 + 2xy.
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Algebra.Com's Answer #851018 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Let x and y be real numbers. Find the maximum value of (x + y)^2,
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\n" ); document.write( "\n" ); document.write( " The solution and the answer in the post by @CPhill are INCORRECT.\r
\n" ); document.write( "\n" ); document.write( " I write this my post to show / (to prove) that they are incorrect.\r
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document.write( "Equation  x^2 + y^2 = 5  + 2xy is equivalent to\r\n" );
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document.write( "   x^2 - 2xy + y^2 = 5,\r\n" );
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document.write( "   (x-y)^2 = 5\r\n" );
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document.write( "   x - y = +/- .\r\n" );
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document.write( "It describes two parallel straight lines in a coordinate plane\r\n" );
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document.write( "    y = x +   and  y = x - .\r\n" );
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document.write( "Moving the abscissa 'x' far enough to the right along x-axis in the positive domain, \r\n" );
document.write( "we can make value of 'x' as big as we like.\r\n" );
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document.write( "Then the value of 'y' becomes big enough.\r\n" );
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document.write( "Hence, the value of (x+y) can be made as big as we want.\r\n" );
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document.write( "Then the value of (x+y)^2 becomes as big as we want and even bigger.\r\n" );
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document.write( "So, expression (x+y)^2  DOES NOT HAVE MAXIMUM  under the given restriction.\r\n" );
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document.write( "ANSWER.  Expression (x+y)^2  DOES NOT HAVE MAXIMUM  under the given restriction.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, proved and disproved.\r
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\n" ); document.write( "\n" ); document.write( " Regarding the post by @CPhill . . . \r
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\n" ); document.write( "\n" ); document.write( "Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.\r
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\n" ); document.write( "\n" ); document.write( "The artificial intelligence is like a baby now. It is in the experimental stage
\n" ); document.write( "of development and can make mistakes and produce nonsense without any embarrassment.\r
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\n" ); document.write( "\n" ); document.write( " It has no feeling of shame - it is shameless.\r
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\n" ); document.write( "\n" ); document.write( "This time, again, it made an error.\r
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\n" ); document.write( "\n" ); document.write( "Although the @CPhill' solution are copy-paste Google AI solutions, there is one essential difference.\r
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\n" ); document.write( "\n" ); document.write( "Every time, Google AI makes a note at the end of its solutions that Google AI is experimental
\n" ); document.write( "and can make errors/mistakes.\r
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\n" ); document.write( "\n" ); document.write( "All @CPhill' solutions are copy-paste of Google AI solutions, with one difference:
\n" ); document.write( "@PChill never makes this notice and never says that his solutions are copy-past that of Google.
\n" ); document.write( "So, he NEVER SAYS TRUTH.\r
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\n" ); document.write( "\n" ); document.write( "Every time, @CPhill embarrassed to tell the truth.\r
\n" ); document.write( "\n" ); document.write( "But I am not embarrassing to tell the truth, as it is my duty at this forum.\r
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\n" ); document.write( "\n" ); document.write( "And the last my comment.\r
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\n" ); document.write( "\n" ); document.write( "When you obtain such posts from @CPhill, remember, that NOBODY is responsible for their correctness,
\n" ); document.write( "until the specialists and experts will check and confirm their correctness.\r
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\n" ); document.write( "\n" ); document.write( "Without it, their reliability is ZERO and their creadability is ZERO, too.\r
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