document.write( "Question 362218: Please solve:
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Algebra.Com's Answer #258141 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There is no solution but we can show why there is no solution.\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "Cube both sides:\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"%28x-1%29%5E2+=+x%5E3\"\r\n" );
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document.write( "\"x%5E2-2x%2B1=x%5E3\"\r\n" );
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document.write( "\"0=x%5E3-x%5E2%2B2x-1\"\r\n" );
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document.write( "We try 1 to see if it is a solution:\r\n" );
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document.write( "1 | 1 -1  2 -1\r\n" );
document.write( "  |    1  0  2 \r\n" );
document.write( "    1  0  2  1\r\n" );
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document.write( "1 is not a solution. However, since all numbers on the \r\n" );
document.write( "bottom row of the synthetic division are non-negative, \r\n" );
document.write( "1 is an upper bound for the solutions.  So any solutions \r\n" );
document.write( "are therefore less than 1.  However any solution less than\r\n" );
document.write( "1 when substituted into the original equation, which is:  \r\n" );
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document.write( "will yield a negative number on the left side.  However\r\n" );
document.write( "the right side is non-negative because the square root\r\n" );
document.write( "radical cannot be a negative number.  Therefore there\r\n" );
document.write( "can be no solution.\r\n" );
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document.write( "We can check that conclusion graphically, heuristically.\r\n" );
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document.write( "Below is the graph of\r\n" );
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document.write( "From which we can see there is no solution for y=0 since\r\n" );
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document.write( "the entire graph is below the x-axis.\r\n" );
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document.write( "\"graph%28400%2C100%2C-5%2C15%2C-2.5%2C2.5%2C%28x-1%29%5E%281%2F3%29+-+sqrt%28x%29%29++\"\r\n" );
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document.write( "Edwin
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