document.write( "Question 268873: find c so that the polynomial will be the square of a bynomial cy2+6y+1 justify your answer \n" ); document.write( "
Algebra.Com's Answer #197145 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
find c so that the polynomial will be the square of a bynomial cy2+6y+1 justify your answer.
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document.write( "Assume A and B are such that\r\n" );
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document.write( "\"%28Ay%2BB%29%5E2=cy%5E2%2B6y%2B1\"\r\n" );
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document.write( "\"%28Ay%2BB%29%28Ay%2BB%29=cy%5E2%2B6y%2B1\"\r\n" );
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document.write( "\"A%5E2y%5E2%2B2ABy%2BB%5E2=cy%5E2%2B6y%2B1\"\r\n" );
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document.write( "To make that an identity we equate like terms on both sides:\r\n" );
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document.write( "\"system%28A%5E2y%5E2=cy%5E2%2C2ABy=6y%2CB%5E2=1%29\"\r\n" );
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document.write( "simplify\r\n" );
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document.write( "\"system%28A%5E2=c%2CAB=3%2CB%5E2=1%29\"\r\n" );
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document.write( "Solving the last equation \r\n" );
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document.write( "\"B%5E2=1\",\r\n" );
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document.write( "\"B%5E2-1=0\"\r\n" );
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document.write( "\"%28B-1%29%28B%2B1%29=0\"\r\n" );
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document.write( "Setting first factor = 0\r\n" );
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document.write( "\"B-1=0\"\r\n" );
document.write( "\"B=1\"\r\n" );
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document.write( "Setting second factor = 0\r\n" );
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document.write( "\"B%2B1=0\"\r\n" );
document.write( "\"B=-1\"\r\n" );
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document.write( "Substituting \"B=1\" in the equation\r\n" );
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document.write( "\"AB=3\"\r\n" );
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document.write( "\"A%2A%281%29=3\"\r\n" );
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document.write( "\"A=3\"\r\n" );
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document.write( "Substituting that in\r\n" );
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document.write( "\"A%5E2=c\"\r\n" );
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document.write( "\"3%5E2=c\"\r\n" );
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document.write( "\"9=c\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"%28Ay%2BB%29%5E2=cy%5E2%2B6y%2B1\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"%283y%2B1%29%5E2=9y%5E2%2B6y%2B1\"\r\n" );
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document.write( "If you use \"B=-1\", you end up with\r\n" );
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document.write( "\"%28-3y-1%29%5E2=9y%5E2%2B6y%2B1\"\r\n" );
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document.write( "Either way, \"C=9\"\r\n" );
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document.write( "Edwin
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