document.write( "Question 212297: How do you find x^2 if x satisfies (x+9)^(1/3)-(x-9)^(1/3)=3 \n" ); document.write( "
Algebra.Com's Answer #160369 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
How do you find \"x%5E2\" if x satisfies \r
\n" ); document.write( "\n" ); document.write( "1. \"%28x%2B9%29%5E%281%2F3%29-%28x-9%29%5E%281%2F3%29=3\"
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document.write( "Let \"A+=+x%2B9\" and \"B=x-9\"\r\n" );
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document.write( "2. \"A%5E%281%2F3%29-B%5E%281%2F3%29=3\"\r\n" );
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document.write( "Cube both sides:\r\n" );
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document.write( "   \"A-3A%5E%282%2F3%29B%5E%281%2F3%29%2B3A%5E%281%2F3%29B%5E%282%2F3%29-B=27\"\r\n" );
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document.write( "Group the first and last terms on the left together\r\n" );
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document.write( "3. \"%28A-B%29-3A%5E%282%2F3%29B%5E%281%2F3%29%2B3A%5E%281%2F3%29B%5E%282%2F3%29=27\"\r\n" );
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document.write( "Notice that \"A-B=%28x%2B9%29-%28x-9%29=x%2B9-x%2B9=18\"\r\n" );
document.write( "Substitute \"18\" for \"A-B\"\r\n" );
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document.write( "\"18-3A%5E%282%2F3%29B%5E%281%2F3%29%2B3A%5E%281%2F3%29B%5E%282%2F3%29=27\"\r\n" );
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document.write( "Subtract 18 from both sides:\r\n" );
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document.write( "\"-3A%5E%282%2F3%29B%5E%281%2F3%29%2B3A%5E%281%2F3%29B%5E%282%2F3%29=9\"\r\n" );
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document.write( "Divide through by \"-3\"\r\n" );
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document.write( "\"A%5E%282%2F3%29B%5E%281%2F3%29-A%5E%281%2F3%29B%5E%282%2F3%29=-3\"\r\n" );
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document.write( "Factor out \"A%5E%281%2F3%29B%5E%281%2F3%29\" on the left\r\n" );
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document.write( "\"A%5E%281%2F3%29B%5E%281%2F3%29%28A%5E%281%2F3%29-B%5E%281%2F3%29%29=-3\"\r\n" );
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document.write( "Using equation 2 above, the parenthetical expression\r\n" );
document.write( "equals 3\r\n" );
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document.write( "\"A%5E%281%2F3%29B%5E%281%2F3%29%283%29=-3\"\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "\"A%5E%281%2F3%29B%5E%281%2F3%29=-1\"\r\n" );
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document.write( "Cube both sides:\r\n" );
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document.write( "\"%28A%5E%281%2F3%29B%5E%281%2F3%29%29%5E3=%28-1%29%5E3\"\r\n" );
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document.write( "\"AB=-1\"\r\n" );
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document.write( "Substitute \"A+=+x%2B9\" and \"B=x-9\", \r\n" );
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document.write( "\"%28x%2B9%29%28x-9%29=-1\"\r\n" );
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document.write( "\"x%5E2-81=-1\"\r\n" );
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document.write( "Add \"81\" to both sides:\r\n" );
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document.write( "\"x%5E2=80\"\r\n" );
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document.write( "That's what you wanted.\r\n" );
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document.write( "Edwin
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