document.write( "Question 1196425: Suppose you are setting up a full-mesh network for x users; and n, the number of two-way connections required to link all users pairwise, must be no greater than 132. For what range of x values can you set up your network?\r
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Algebra.Com's Answer #829246 by ikleyn(52868) $\"\"$ $\"About$

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\n" ); document.write( "Suppose you are setting up a full-mesh network for x users;
\n" ); document.write( "and n, the number of two-way connections required to link all users pairwise,
\n" ); document.write( "must be no greater than 132. For what range of x values can you set up your network?
\n" ); document.write( "x(x-1)/2=n
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document.write( "They want you solve this inequality\r\n" );
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document.write( "     <= 132\r\n" );
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document.write( "in positive integer numbers.\r\n" );
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document.write( "So, you multiply both sides by 2\r\n" );
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document.write( "    x*(x-1) <= 2*132 = 264.\r\n" );
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document.write( "At this point, you can estimate x by noticing that   = 16.24...  (rounded.\r\n" );
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document.write( "Hence, integer x  must be closest to it lesser integer .\r\n" );
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document.write( "        CHECK.  16*(16-1) = 16*15 = 240,  while 17*16 = 272, confirming this answer.\r\n" );
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document.write( "Alternatively, you can solve quadratic inequality\r\n" );
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document.write( "    x^2 - x - 264 <= 0,\r\n" );
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document.write( "and for x you will get\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "Thus  -15.755 <= x <= 16.755,  and since we want x be positive integer number, it gives the same answer x <= 16.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in two ways for your better understanding, giving the ANSWER n <= 16.\r
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