document.write( "Question 1209552: If x = (19 + 8√3)^(½)
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Algebra.Com's Answer #849415 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "If x = (19 + 8√3)^(1/2), find $\"%28x%5E4+-+6x%5E3+-+2x%5E2+%2B+18x+%2B+23%29%2F%28x%5E2+-+8x+%2B+15%29\"$ .
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document.write( "(1)   = .\r\n" );
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document.write( "         To check and to prove, simply square right side.  You will get then  .\r\n" );
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document.write( "(2)  So, x = .  \r\n" );
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document.write( "         It implies  x-4 = ,  (x-4)^2 = 3,  x^2 - 8x + 16 = 3,  x^2 - 8x + 13 = 0.\r\n" );
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document.write( "(3)  Let's calculate the denominator  x^2 - 8x + 15.\r\n" );
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document.write( "         It is  x^2 -8x + 15 = (x^2 - 8x + 13) + 2.\r\n" );
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document.write( "         The part in parentheses is zero, so  the denominator  x^2 - 8x + 15  is simply  2.\r\n" );
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document.write( "(4)  In principle, the numerator can be calculated directly, but it is computationally boring procedure.\r\n" );
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document.write( "     It is simpler to perform a long division.\r\n" );
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document.write( "            = x^2 + 2x - 1 +  = \r\n" );
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document.write( "         = x^2 + 2x - 1 +  = (x^2 + 2x - 1) + (19 - 10x) = x^2 - 8x + 18 = (x^2 - 8x + 13) + 5.\r\n" );
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document.write( "(5)  The value in the parentheses is zero, as we established above.\r\n" );
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document.write( "     So, we get the \r\n" );
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document.write( "ANSWER.  If  x = (19 + 8√3)^(1/2),  then    is equal to 5.\r\n" );
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