document.write( "Question 1117121: if x^2 -16√(x) =12 then x-2√(x) = ?? \n" ); document.write( "

Algebra.Com's Answer #732153 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Let me introduce new variable  u = .\r\n" );
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document.write( "Then I can reformulate the problem in this EQUIVALENT way:\r\n" );
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document.write( "    If   = ,  then find  .\r\n" );
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document.write( "If   = ,   then\r\n" );
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document.write( "     = 0.    (1)\r\n" );
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document.write( "The left side can be factored:\r\n" );
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document.write( "     = .\r\n" );
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document.write( "into the product of two quadratic polynomials.  (You may check the validity of this decomposition on your own).\r\n" );
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document.write( "Thus the equation (1) is equivalent to\r\n" );
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document.write( "    . = 0.     (2)\r\n" );
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document.write( "If \"u\" is the real root of the equation (1),  then \"u\" is the real root of the equation (2).\r\n" );
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document.write( "But the second polynomial (second multiplier)    is positively defined quadratic function  ,  which has NO real roots.\r\n" );
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document.write( "Therefore, \"u\" is the root of the first trinomial  of (2),  i.e.\r\n" );
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document.write( "     = 0,\r\n" );
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document.write( "Then   =  =  = .\r\n" );
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document.write( "Now, if   = ,  then   =  =  = 2.\r\n" );
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document.write( "     If   = ,  then   =  =  = 2.\r\n" );
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document.write( "    \r\n" );
document.write( "Thus in any case   = 2.\r\n" );
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document.write( "It is the answer to the problem question.\r\n" );
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document.write( "Answer.  If x is a real number such as   = ,  then   = 2.\r\n" );
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