document.write( "Question 1166829: The product of the smallest and largest of three consecutive even integers is three times the middle integer. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #791375 by ikleyn(52809) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let x be the middle of the three consecutive even integers.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then (x-2) and (x+2) are two other \"extreme\" integers.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation, from the condition, is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (x-2)*(x+2) = 3x,  or\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 4     = 3x\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 3x - 4 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor left side\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (x-4)*(x+1) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of the two roots x= 4 and x= -1, only x= 4 satisfies the condition to be even integer number.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The numbers are 2, 4 and 6.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );