document.write( "Question 1206590: If 3n³× (n-2)! + 6n - 3n² × (n-3)! - 360 = 0 , find value of n ? \n" ); document.write( "

Algebra.Com's Answer #844151 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "If 3n³× (n-2)! + 6n - 3n² × (n-3)! - 360 = 0 , find value of n ?
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document.write( "   +  -  - 360 =\r\n" );
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document.write( "= .. + 6n - 360.\r\n" );
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document.write( "Now you can see that this expression is monotonically growing function of n.\r\n" );
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document.write( "So, if we guess one solution, it will provide a UNIQUE solution.\r\n" );
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document.write( "It is not difficult to guess one solution. It is n= 4, because\r\n" );
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document.write( "    .. + 6*4 - 360 = 3*16*7*1 + 24 - 360 = 0.\r\n" );
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document.write( "So, the ANSWER to the problem is n= 4.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In such problems, guessing of a root in combinations with monotonicity
\n" ); document.write( "of a function turns guessing in strict mathematical proof.\r
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\n" ); document.write( "\n" ); document.write( "In other words, in this combination, guessing of a root acquires
\n" ); document.write( "the force and the status of a valid mathematical proof.\r
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