Algebra.Com's Answer #722113 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "I am familiar with this problem . . . \r
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document.write( "It was posted to the forum a week or two ago, and I solved it . . . \r
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document.write( "So, I know that the formulation in THIS post IS NOT EXACTLY PRECISE.\r
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document.write( "Therefore, I edited it, and the EDITED formulation (the only correct, valid and right version) is THIS:\r
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document.write( " Evaluate  \r\n" );
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document.write( "Below is the solution:\r
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document.write( "Let us consider, for brewity of writing, more general expression\r\n" );
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document.write( " = x, (1)\r\n" );
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document.write( "where a =  , b =  . Square (1) (both sides). You will get then \r\n" );
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document.write( " =  ,\r\n" );
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document.write( " =  . (2)\r\n" );
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document.write( "Square (2) (both sides). You will get then\r\n" );
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document.write( " =  . (3)\r\n" );
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document.write( " =  . (4)\r\n" );
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document.write( "Notice that the right side of the expression (4) is the same as the given expression, so it is equal to x. Thus you have \r\n" );
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document.write( " = x. \r\n" );
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document.write( "It is equivalent to\r\n" );
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document.write( " -  = x, or\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Now substitute here a = , b = . You will get this equation in the form\r\n" );
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document.write( " = 0, or, multiplying all the terms by 3\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "The plot of the last polynomial is shown below.\r\n" );
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document.write( "Plot y =  \r\n" );
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document.write( "It clearly shows that x= 1 and x= 2 are the roots. Having this HINT, you can check it MANUALLY (as I did . . . ).\r\n" );
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document.write( "The two other roots of the polynomial are complex numbers.\r\n" );
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document.write( "Since the value of  is, obviously, real number greater than 1, it can be only 2.\r\n" );
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document.write( "It proves that = 2.\r\n" );
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document.write( "Answer. = 2.\r\n" );
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document.write( "Check.  = 1.984 (approximately).\r\n" );
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document.write( "---------------
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document.write( "See the lesson\r
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document.write( " - Evaluating expressions that contain infinitely many square roots\r
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document.write( "in this site.\r
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