document.write( "Question 1107598: Find the relationship between Q and R so that X³+3PX²+QX+R shall be a perfect cube for all values of X \n" ); document.write( "
Algebra.Com's Answer #722595 by AnlytcPhil(1806)\"\" \"About 
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document.write( "Let S be such that\r\n" );
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document.write( "X³+3PX²+QX+R = (X+S)³\r\n" );
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document.write( "X³+3PX²+QX+R = X³+3X²S+3XS²+S³\r\n" );
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document.write( "Each term in a power of X on the left must equal \r\n" );
document.write( "identically to the corresponding power of X on the \r\n" );
document.write( "right side, and also the corrsponding constant terms \r\n" );
document.write( "must also be equal:\r\n" );
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document.write( "X³ = X³,  3PX² = 3X²S,  QX = 3XS²,  R = S³\r\n" );
document.write( "            3P = 3S      Q = S²     \r\n" );
document.write( "             P = S\r\n" );
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document.write( "Multiply equals by equals using P = S and Q = S²\r\n" );
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document.write( "PQ = S³\r\n" );
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document.write( "And since also R = S³,\r\n" );
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document.write( "PQ = R   <-- answer.\r\n" );
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document.write( "Edwin
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