document.write( "Question 1195271: Let P(x)=2009x^9+a₁x^8+...+a₉ such that
\n" ); document.write( " $\"P%281%2Fn%29=1%2F%28n%5E3%29\"$ , n = 1,2,...,9.
\n" ); document.write( "Find $\"P%281%2F10%29\"$ . \n" ); document.write( "

Algebra.Com's Answer #827704 by ikleyn(52793) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Let P(x) = 2009x^9 + a₁x^8 + . . . + a₉ such that
\n" ); document.write( " $\"P%281%2Fn%29=1%2F%28n%5E3%29\"$ , n = 1,2,...,9.
\n" ); document.write( "Find $\"P%281%2F10%29\"$ .
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\n" ); document.write( "\n" ); document.write( "            The solution by @MathLover1 is INCORRECT and IRRELEVANT.\r
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\n" ); document.write( "\n" ); document.write( "            Do not spend your time looking in it; I also will not spend my and your time,\r
\n" ); document.write( "\n" ); document.write( "            explaining why it is wrong and irrelevant.\r
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\n" ); document.write( "\n" ); document.write( "            Simply madam does not understand the problem, does not know the subject\r
\n" ); document.write( "\n" ); document.write( "            and is not in the theme.\r
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\n" ); document.write( "\n" ); document.write( "            Read my solution below.\r
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document.write( "You are given a polynomial P(x) of degree 9 with the leading coefficient 2009;\r\n" );
document.write( "all 9 coefficients of lower degrees are unknown.\r\n" );
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document.write( "You also are given the values of the polynomial in 9 points\r\n" );
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document.write( "    P(1) = 1,   = ,   = , . . . ,  = .\r\n" );
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document.write( "Consider another polynomial\r\n" );
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document.write( "    Q(x) =  + .\r\n" );
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document.write( "This polynomial has the degree of 9 and has the same values  1,  ,  , . . . , \r\n" );
document.write( "in all 9 given points  1,  ,  , . . . , ,  as polynomial P(x) has.  \r\n" );
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document.write( "You can easily see it from the formula.\r\n" );
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document.write( "    In addition, polynomial Q(X) has the same value \r\n" );
document.write( "    of the leading coefficient 2009 as polynomial P(X) has.\r\n" );
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document.write( "It    that polynomials P(x) and Q(X) are identical as polynomials of x.\r\n" );
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document.write( "THEREFORE,   =  =  + .\r\n" );
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document.write( "      This expression is the      to the problem.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered, explained and completed.\r
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\n" ); document.write( "\n" ); document.write( "This problem is of a Math Olympiad level or an advanced Math Circle level,\r
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\n" ); document.write( "\n" ); document.write( "and my solution is written adequately to this level.\r
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