document.write( "Question 658134: one of the root of the equation x^2-px+q=0 is the square of the other.proof that pq-q(3p+1)-q^2=0 \n" ); document.write( "
Algebra.Com's Answer #410226 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'm sorry but what you are asked to prove is\r\n" );
document.write( "simply not true.  Here is why:\r\n" );
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document.write( "Take the equation\r\n" );
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document.write( "x² - 6x + 8 = 0\r\n" );
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document.write( "Solving it by factoring the left side:\r\n" );
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document.write( "(x - 2)(x - 4) = 0\r\n" );
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document.write( "x - 2 = 0;  x - 4 = 0\r\n" );
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document.write( "    x = 2;      x = 4\r\n" );
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document.write( "So one root is 2 and the other root is 4\r\n" );
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document.write( "Since 4 is the square of 2, the equation\r\n" );
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document.write( "x² - 6x + 8 = 0 fulfills the requirements that\r\n" );
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document.write( "one of the roots is the square of the other.  \r\n" );
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document.write( "So if we compare it to:\r\n" );
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document.write( "x² - px + q = 0\r\n" );
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document.write( "We see that p=6 and q=8.\r\n" );
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document.write( "So if what you are asked to prove were true, then\r\n" );
document.write( "this \r\n" );
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document.write( "  pq-q(3p+1)-q² = 0 \r\n" );
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document.write( "would have to be true when we substitute p=6 and q=8\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "6·8-8(3·6+1)-8² = 0\r\n" );
document.write( "  48-8(18+1)-64 = 0\r\n" );
document.write( "    48-8(19)-64 = 0\r\n" );
document.write( "      48-152-64 = 0\r\n" );
document.write( "           -168 = 0\r\n" );
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document.write( "But as you see, this is not true at all.  So the \r\n" );
document.write( "problem is botched.  If you can correct it in\r\n" );
document.write( "the thank-you note, we will help you.\r\n" );
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document.write( "Edwin
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