document.write( "Question 1144876: One root of the equation ax^2 + 2bx + c = 0 is the reciprocal of the square of the other root. Show that a^3 +c^3 +2abc=0. \n" ); document.write( "
Algebra.Com's Answer #766060 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
\"ax%5E2+%2B+2bx+%2B+c+=+0\" \r\n" );
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document.write( "Let r be one root.  Then the other root is 1/r²\r\n" );
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document.write( "We know that the constant term of a quadratic divided by the leading\r\n" );
document.write( "coefficient equals the product of the roots.\r\n" );
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document.write( "So the product of the two roots is c/a, therefore\r\n" );
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document.write( "\"%28r%29%281%2Fr%5E2%29=c%2Fa\"\r\n" );
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document.write( "\"1%2Fr=c%2Fa\"\r\n" );
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document.write( "\"a=rc\"\r\n" );
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document.write( "\"a%2Fc=r\"\r\n" );
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document.write( "So a/c is a root and must satisfy the original equation:\r\n" );
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document.write( "\"a%28a%2Fc%29%5E2+%2B+2b%28a%2Fc%29+%2B+c+=+0\"\r\n" );
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document.write( "\"a%28a%5E2%2Fc%5E2%29+%2B+2ab%2Fc+%2B+c+=+0\"\r\n" );
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document.write( "\"a%5E3%2Fc%5E2%2B2ab%2Fc%2Bc=0\"\r\n" );
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document.write( "\"a%5E3%2B2abc%2Bc%5E3=0\"\r\n" );
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document.write( "\"a%5E3%2Bc%5E3%2B2abc=0\"\r\n" );
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document.write( "Edwin
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