document.write( "Question 205527: okay i had a math problem in class today and this isn't from a textbook
\n" ); document.write( "here it is
\n" ); document.write( "Input----Output
\n" ); document.write( " 1------ 4
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Algebra.Com's Answer #155153 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
okay i had a math problem in class today and this isn't from a textbook
\n" ); document.write( "here it is
\n" ); document.write( "Input----Output
\n" ); document.write( " 1------ 4
\n" ); document.write( " 2------ 8
\n" ); document.write( " 3------ 24
\n" ); document.write( " 4------ X\r
\n" ); document.write( "\n" ); document.write( "Solve X, and the answer is not 4, 96, or 32. Please Help me ASAP!!!!!
\n" ); document.write( "
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document.write( "Use a quadratic polynomial in n:\r\n" );
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document.write( "When the Input is n, assume the Output is \"An%5E2+%2B+Bn+%2B+C\".\r\n" );
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document.write( "Substituting the given data:\r\n" );
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document.write( "When the Input is 1, the Output is \"A%281%29%5E2+%2B+B%281%29+%2B+C=A%2BB%2BC=4\".\r\n" );
document.write( "When the Input is 2, the Output is \"A%282%29%5E2+%2B+B%282%29+%2B+C=4A%2B2B%2BC=8\".\r\n" );
document.write( "When the Input is 3, the Output is \"A%283%29%5E2+%2B+B%283%29+%2B+C=9A%2B3B%2BC=24\".\r\n" );
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document.write( "So we solve the system of equations:\r\n" );
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document.write( "\"system%28A%2BB%2BC=4%2C4A%2B2B%2BC=8%2C9A%2B3B%2BC=24%29\"\r\n" );
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document.write( "Solve that system by any method you know, and get\r\n" );
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document.write( "\"A=6\", \"B=-14\", and \"C=12\"\r\n" );
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document.write( "So the expression\r\n" );
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document.write( "\"An%5E2+%2B+Bn+%2B+C\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"6n%5E2+-+14n+%2B+12\". Therefore, to check the first three terms in\r\n" );
document.write( "the equation to see if it is correct:\r\n" );
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document.write( "When the Input is 1, the Output is \"6%281%29%5E2+-+14%281%29+%2B+12=6-14%2B12=4\".\r\n" );
document.write( "When the Input is 2, the Output is \"6%282%29%5E2+-+14%282%29+%2B+12=24-28%2B12=8\".\r\n" );
document.write( "When the Input is 3, the Output is \"6%283%29%5E2+-+14%283%29+%2B+12=54-42%2B12=24\".\r\n" );
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document.write( "Those are correct, so to get the next term we substitute n=4:\r\n" );
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document.write( "When the Input is 4, the Output is \"6%284%29%5E2+-+14%284%29+%2B+12=96-56%2B12=52\".\r\n" );
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document.write( "Edwin
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