document.write( "Question 1031664: Find all the real solution of the equation
\n" ); document.write( "x^2-|x-1|-3=0 \n" ); document.write( "

Algebra.Com's Answer #646348 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"x%5E2+-+abs%28x-1%29+-+3\"$ = $\"0\"$ . (1)\r
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document.write( "1. Consider the domain x >= 1.\r\n" );
document.write( "   In this domain |x-1| = x-1,\r\n" );
document.write( "   and yours equation (1) becomes\r\n" );
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document.write( "    = ,  or\r\n" );
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document.write( "    = ,\r\n" );
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document.write( "   (x-2)*(x+1) = 0\r\n" );
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document.write( "   with the roots x = 2 and x = -1.\r\n" );
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document.write( "   Of them, only x = 2 belongs to the domain x >= 1.\r\n" );
document.write( "   So, x = 2 is the ONLY solution of the equation (1) in this domain.\r\n" );
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document.write( "2. Next, consider the domain x < 1.\r\n" );
document.write( "   In this domain |x-1| = -(x-1). \r\n" );
document.write( "   and yours equation (1) becomes\r\n" );
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document.write( "    = ,  or\r\n" );
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document.write( "    = .\r\n" );
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document.write( "   Find the roots using the quadratic formula.\r\n" );
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document.write( "    = ,   = .\r\n" );
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document.write( "   Of them, only  =  belongs to the domain x < 1.\r\n" );
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document.write( "   So,  =   is the ONLY solution of the equation (1) in this domain.\r\n" );
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document.write( "Answer.  The solutions are  x = 2  and  x = .\r\n" );
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