document.write( "Question 1093850: Please help me solve:
\n" ); document.write( "x(x+2)(x+4)(x+6)+16=0 \n" ); document.write( "
Algebra.Com's Answer #708462 by ikleyn(52802)\"\" \"About 
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document.write( "Introduce new variable  y = x-3  (the central point for the sequence x, x+2, x+4, x+6).\r\n" );
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document.write( "Then your equation takes the form\r\n" );
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document.write( "(y-3)*(y-1)*(y+1)*(y+3) = -16,   or\r\n" );
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document.write( "\"%28y%5E2-9%29%2A%28y%5E2-1%29\" = -16,\r\n" );
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document.write( "\"y%5E4+-+10y%5E2+%2B+25\" = 0,\r\n" );
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document.write( "\"%28y%5E2-5%29%5E2\" = 0,\r\n" );
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document.write( "which implies  \"y%5E2\" = 5,  and hence  y = +/- \"sqrt%285%29\".\r\n" );
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document.write( "Answer.  The original equation has the solutions  x = \"3%2Bsqrt%285%29\" and  \"3-sqrt%285%29\", each of multiplicity 2.\r\n" );
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document.write( "    The problem has a hidden symmetry around the central point.\r\n" );
document.write( "    When written at variables centered at this point, the symmetry becomes explicit and facilitates the problem' solution.\r\n" );
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