document.write( "Question 1152853: $\"w%5E3=1\"$ , Find the exact values of $\"%281%2B2w%2B3w%5E2%29\"$ & $\"%281%2B3w%2B2w%5E2%29\"$ , given that these are roots of the eq'n or $\"%281%2B3w%2B2w%5E2%29\"$ ?\r
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Algebra.Com's Answer #774979 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "No complex imaginary number can be said to be \"larger\" or \"smaller\" than any\r\n" );
document.write( "other complex numbers.  Only real numbers can be said to be larger or smaller\r\n" );
document.write( "than other real numbers.  \r\n" );
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document.write( "We should do all the possibilities.\r\n" );
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document.write( "The problem from the very beginning:\r\n" );
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document.write( "Since \r\n" );
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document.write( "and\r\n" );
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document.write( "are roots of the equation \r\n" );
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document.write( "their sum is equal to the coefficient of x with the opposite sign:\r\n" );
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document.write( "So:\r\n" );
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document.write( "or\r\n" );
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document.write( "[We can check that their product will be the constant term 3, but\r\n" );
document.write( "we don't need that.\r\n" );
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document.write( "(1) When we substitute \r\n" );
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document.write( "into \r\n" );
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document.write( "we get\r\n" );
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document.write( "-----\r\n" );
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document.write( "(2)  When we substitute \r\n" );
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document.write( "into \r\n" );
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document.write( "we get\r\n" );
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document.write( "(3) When we substitute \r\n" );
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document.write( "into \r\n" );
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document.write( "we get the value\r\n" );
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document.write( "(4) When we substitute \r\n" );
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document.write( "into \r\n" );
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document.write( "we get the value\r\n" );
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document.write( "---\r\n" );
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document.write( "So, the exact values of both   and , \r\n" );
document.write( "given that\r\n" );
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document.write( "and\r\n" );
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document.write( "are roots of the equation\r\n" );
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document.write( "Note that for , the sign of the imaginary part is\r\n" );
document.write( "OPPOSITE the sign of the imaginary part of what is substituted, and\r\n" );
document.write( "that for , the sign of the imaginary part is the \r\n" );
document.write( "SAME AS the sign of the imaginary part of what is substituted.\r\n" );
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document.write( "Edwin

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