document.write( "Question 265347: The square of the first of three consecutive odd integers is 9 more than 6 times the sum of the second and the first. Find the numbers.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #854017 by ikleyn(53750) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The square of the first of three consecutive odd integers is 9 more than 6 times the sum of the second and the first.
\n" ); document.write( "Find the numbers.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The solution in the post by @mananth is incorrect. His answer is incorrect, as well.\r
\n" ); document.write( "\n" ); document.write( " See below my correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let the three consecutive odd integer numbers be x, (x+2) and (x+4).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation is\r\n" );
document.write( "\r\n" );
document.write( "    x^2 = 6(x + (x+2)) + 9,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Write it in standard form quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 12x - 21 = 0.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its discriminant is\r\n" );
document.write( "\r\n" );
document.write( "    d = b^2 - 4ac = (-12)^2 -4*1*(-21) = 144 + 84 = 228.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number 228 is not a perfect square.\r\n" );
document.write( "\r\n" );
document.write( "It tells that equation (1) has no solutions in integer numbers.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "The conclusion is that the given problem has no solutions and describes a situation which NEVER may happen.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In other words, the problem as it is given in the post is a FAKE.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );