document.write( "Question 1026395: The product of two consecutive odd integers is 6 more than 5 times the smaller number, find both numbers \n" ); document.write( "

Algebra.Com's Answer #853901 by ikleyn(53646) $\"\"$ $\"About$

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\n" ); document.write( "The product of two consecutive odd integers is 6 more than 5 times the smaller number, find both numbers
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\n" ); document.write( "\n" ); document.write( "        The \"solution\" in the post by @mananth is INCORRECT,\r
\n" ); document.write( "\n" ); document.write( "        since he incorrectly solved the quadratic equation.\r
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\n" ); document.write( "\n" ); document.write( "        See my reasoning below.\r
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document.write( "Let 'n' be the smaller of the two odd consecutive integers.\r\n" );
document.write( "Then the greater add consecutive integer is (n+2).\r\n" );
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document.write( "Our equation is\r\n" );
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document.write( "    n*(n+2) = 5n + 6,\r\n" );
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document.write( "    n^2 + 2n = 5n + 6,\r\n" );
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document.write( "    n^2 - 3n - 6 = 0.\r\n" );
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document.write( "The discriminant is  d =  b^2 - 4ac = (-3)^2 - 4*1*(-6) = 9 + 24 = 33.\r\n" );
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document.write( " =   is not an integer or a rational number, \r\n" );
document.write( "so integer 'n' as described in the problem, does not exist.\r\n" );
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document.write( "ANSWER.  As posed/printed/presented in the post, the problem HAS NO solution.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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