document.write( "Question 1207632: Find the real solutions of each equation.\r
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\n" ); document.write( "\n" ); document.write( "Let rt = root \r
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\n" ); document.write( "\n" ); document.write( "1. x^2 - 3x - rt{x^2 - 3x} = 2\r
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\n" ); document.write( "\n" ); document.write( "2. 3x^(3/4) + 5x^(2/3) - 2 = 0 \n" ); document.write( "

Algebra.Com's Answer #845605 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " In this my post, I will solve equation 1, ONLY.\r
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document.write( "    x^2 - 3x -  = 2.    (1)\r\n" );
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document.write( "It is a standard equation to solve using \"change of a variable\".\r\n" );
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document.write( "So, we introduce new variable  y = .\r\n" );
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document.write( "Then equation (1) takes the form\r\n" );
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document.write( "    y^2 - y = 2,\r\n" );
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document.write( "or\r\n" );
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document.write( "    y^2 - y - 2 = 0.\r\n" );
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document.write( "We look for non-negative solutions of this equation.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (y+1)*(y-2) = 0\r\n" );
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document.write( "and get two roots y= -1  and  y= 2.\r\n" );
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document.write( "For what follows, we consider only positive value y= 2.\r\n" );
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document.write( "The root y= 2  leads  to equation \r\n" );
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document.write( "    x^2 - 3x = 4,\r\n" );
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document.write( "    x^2 - 3x - 4 = 0,\r\n" );
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document.write( "    (x-4)*(x+1) =  0   with the solutions  x= 4  and x= -1.\r\n" );
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document.write( "Of these two solutions, both work. \r\n" );
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document.write( "ANSWER.  There are two real solutions for x: they are  x= -1  and  x= 4.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Please do not pack more than one problem per post.\r
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