document.write( "Question 1152545: 4x − 11x^1/2 + 6 = 0
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Algebra.Com's Answer #774573 by ikleyn(52786)\"\" \"About 
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document.write( "Introduce new variable  y = \"sqrt%28x%29\".\r\n" );
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document.write( "Then your equation takes the form\r\n" );
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document.write( "    4y^2 - 11y + 6 = 0.\r\n" );
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document.write( "Solve this quadratic equation using the quadrtic formula\r\n" );
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document.write( "    \"y%5B1%2C2%5D\" = \"%2811+%2B-+sqrt%28%28-11%29%5E2+-+4%2A4%2A6%29%29%2F%282%2A4%29\" = \"%2811+%2B-+sqrt%2825%29%29%2F8\" = \"%2811+%2B-+5%29%2F8\".\r\n" );
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document.write( "Case 1.  \"y%5B1%5D\" = \"%2811%2B5%29%2F8\" = \"16%2F8\" = 2.\r\n" );
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document.write( "         Then  \"sqrt%28x%29\" = 2;  hence,  x = 4.\r\n" );
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document.write( "Case 2.  \"y%5B2%5D\" = \"%2811-5%29%2F8\" = \"6%2F8\" = \"3%2F4\".\r\n" );
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document.write( "         Then  \"sqrt%28x%29\" = \"3%2F4\";  hence,  x = \"9%2F16\".\r\n" );
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document.write( "ANSWER.  The given equation has two and only two solutions:  x= 4  and  x= \"9%2F16\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Introducing new variable is a standard way of solving such equations.\r
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