document.write( "Question 1205857: Find x,
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Algebra.Com's Answer #842931 by ikleyn(52790)\"\" \"About 
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document.write( "Your starting equation is\r\n" );
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document.write( "    \"%287%2Bsqrt%28x%29%29%5E%281%2F3%29\" + \"%287-sqrt%28x%29%29%5E%281%2F3%29\" = 2.    (1)\r\n" );
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document.write( "Let  a = \"%287%2Bsqrt%28x%29%29%5E%281%2F3%29\";  b = \"%287-sqrt%28x%29%29%5E%281%2F3%29\".\r\n" );
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document.write( "Raise both sides of equation (1) to degree 3.\r\n" );
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document.write( "Use\r\n" );
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document.write( "    \"%28a+%2B+b%29%5E3\" = \"a%5E3+%2B+b%5E3\" + 3ab*(a+b),\r\n" );
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document.write( "    \"a%5E3+%2B+b%5E3\" = \"%287%2Bsqrt%28x%29%29\"  + \"%287-sqrt%28x%29%29\" = 14,\r\n" );
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document.write( "    a + b = 2   <<<---===  given by equation,\r\n" );
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document.write( "    ab = \"%2849+-+x%29%5E%281%2F3%29\".\r\n" );
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document.write( "You will get\r\n" );
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document.write( "    \"14+%2B+3%2A%2849-x%29%5E%281%2F3%29%2A2\" = 8.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    \"%2849+-+x%29%5E%281%2F3%29\" = \"%288-14%29%2F6\",\r\n" );
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document.write( "    \"%2849+-+x%29%5E%281%2F3%29\" = -1.\r\n" );
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document.write( "Raise both sides of the last equation to degree 3\r\n" );
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document.write( "    49 - x = -1,\r\n" );
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document.write( "    49 + 1 = x,\r\n" );
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document.write( "     x     = 50.\r\n" );
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document.write( "ANSWER.  x = 50.\r\n" );
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document.write( "CHECK.   \"%287+%2B+sqrt%2850%29%29%5E%281%2F3%29\" + \"%287+-+sqrt%2850%29%29%5E%281%2F3%29\" = 2.414213562 + (-0.414213562) = 2.0000000\r\n" );
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