Algebra.Com's Answer #848902 by ikleyn(52832)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Given that x and y are integers and  , find x-y.
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document.write( "Your starting equation is \r\n" );
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document.write( "  =  .\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "  + 11 =  +  +  .\r\n" );
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document.write( "Now we want to follow the problem's instruction and find the solution \r\n" );
document.write( "in integer numbers x and y. For it, we combine irrationalities containing square roots \r\n" );
document.write( "in one equation and combine all the rest in the other equation.\r\n" );
document.write( "Doing this way, you will get these two equations to find two unknown integer x and y\r\n" );
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document.write( "  =  ,\r\n" );
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document.write( " 11 = +  +  .\r\n" );
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document.write( "Then trial and error will lead you to the unique solution x= 1, y= 9 in integer numbers.\r\n" );
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document.write( "It gives then x - y = 1 - 9 = -8.\r\n" );
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document.write( "ANSWER. x - y = -8.\r\n" );
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document.write( "Final CHECK: Left side = use your calculator = 4.16227766 (approximately).\r\n" );
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document.write( " Right side =  =  = use your calculator = 4.16227766.\r\n" );
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document.write( " * * * All the digits coincide - hence, the solution is PRECISELY CORRECT ! * * * \r\n" );
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document.write( "Solved.\r
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document.write( "Notice that if the problem does not require x and y to be integer numbers,
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document.write( "then the given equation would have infinitely many solutions for two unknowns x and y in real numbers.\r
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document.write( "Thus, the requirement for the solutions of this equation to be integer numbers
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document.write( "extracts/identifies a unique solution among an infinite number of other possible real solutions.\r
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document.write( " This is of EXTREME IMPORTANCE ( ! )\r
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