document.write( "Question 353546: PLEASE HELP ME TO SOLVE THESE QUESTIONS.............\r
\n" ); document.write( "\n" ); document.write( "Q1.IF \"x%5E3%2B1%2Fx%5E3=2\" then find the value of x+1/x\r
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Algebra.Com's Answer #252631 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
PLEASE HELP ME TO SOLVE THESE QUESTIONS.............\r
\n" ); document.write( "\n" ); document.write( "Q1.IF \"x%5E3%2B1%2Fx%5E3=2\" then find the value of x+1/x
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document.write( "Using the binomial theorem:\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3=x%5E3%2B3x%5E2%281%2Fx%29%2B3x%281%2Fx%29%5E2%2B%281%2Fx%29%5E3%29\"\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3=x%5E3%2B3x%2B3x%281%2Fx%5E2%29%2B1%2Fx%5E3\"\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3=x%5E3%2B3x%2B3%2Fx%2B1%2Fx%5E3\"\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3=x%5E3%2B1%2Fx%5E3%2B3x%2B3%2Fx\"\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3=%28x%5E3%2B1%2Fx%5E3%29%2B3%28x%2B1%2Fx%29\"\r\n" );
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document.write( "and since we are given \"x%5E3%2B1%2Fx%5E3=2\",\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3=2%2B3%28x%2B1%2Fx%29\"\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E3-3%28x%2B1%2Fx%29-2=0\"\r\n" );
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document.write( "Let \"y+=+x%2B1%2Fx\", which is what we want to find.\r\n" );
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document.write( "\"y%5E3-3y-2=0\"\r\n" );
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document.write( "Feasible rational roots are ±1, ±2\r\n" );
document.write( "Using synthetic division we find that -1 is a solution\r\n" );
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document.write( "-1|1  0 -3 -2\r\n" );
document.write( "  |  -1  1  2\r\n" );
document.write( "   1 -1 -2  0\r\n" );
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document.write( "Thus we have factored\r\n" );
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document.write( "\"y%5E3-3y-2=0\"\r\n" );
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document.write( "as\r\n" );
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document.write( "\"%28y%2B1%29%28y%5E2-y-2%29=0\"\r\n" );
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document.write( "Factoring further:\r\n" );
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document.write( "\"%28y%2B1%29%28y%2B1%29%28y-2%29=0\"\r\n" );
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document.write( "Thus the solutions are y = -1, y = 2\r\n" );
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document.write( "so \"x%2B1%2Fx\" is either -1 or 2.\r\n" );
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\n" ); document.write( "Q2.FIND THE VALUE OF \"%28x%2By%29%5E3%2B%28x-2y%2B2%29\"\r
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document.write( "Something is missing from this one that must be given \r\n" );
document.write( "to find a solution.  Check the problem again and repost \r\n" );
document.write( "it with the part that's missing here.\r\n" );
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\n" ); document.write( "Q3.IF .then find the value of \"x%5E16\"
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document.write( "Multiplying the first two factors:\r\n" );
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document.write( "Multiplying the first two factors:\r\n" );
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document.write( "\"%28x%5E4-1%2Fx%5E4%29%2A%28x%5E4%2B1%2Fx%5E4%29%2A%28x%5E8%2B1%2Fx%5E8%29=3%2F2\"\r\n" );
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document.write( "Multiplying the first two factors:\r\n" );
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document.write( "\"%28x%5E8-1%2Fx%5E8%29%2A%28x%5E8%2B1%2Fx%5E8%29=3%2F2\"\r\n" );
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document.write( "Multiplying those factors:\r\n" );
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document.write( "\"x%5E16-1%2Fx%5E16=3%2F2\"\r\n" );
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document.write( "Let \"y+=+x%5E16\"\r\n" );
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document.write( "\"y-1%2Fy=3%2F2\"\r\n" );
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document.write( "Clear of fractions:\r\n" );
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document.write( "\"2y%5E2-2=3y\"\r\n" );
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document.write( "\"2y%5E2-3y-2=0\"\r\n" );
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document.write( "Factoring,\r\n" );
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document.write( "\"%28y-2%29%282y%2B1%29=0\"\r\n" );
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document.write( "Solutions are \"y+=+2\", \"y=-1%2F2\"\r\n" );
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document.write( "and since \"y=x%5E16\"\r\n" );
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document.write( "\"x%5E16=2\" or \"x%5E16=-1%2F2\"\r\n" );
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document.write( "(In the case of the second negative solution, \r\n" );
document.write( "x would have to be imaginary).\r\n" );
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document.write( "Edwin

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