document.write( "Question 1094808: If the sum of three number in geometric series is 14 and their product is 64.find the number \n" ); document.write( "

Algebra.Com's Answer #709390 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "2, 4 and 8. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Another progression is 8, 4, 2.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Mental solution. 3 seconds.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------
\n" ); document.write( "If you want algebra solution, here it is.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let \"a\" be the first term and \"r\" be the common ratio.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the terms are  a, ar and ar^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "a + ar + ar^2 = 14,     (1)\r\n" );
document.write( "a * ar * ar^2 = 64      (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (2) you have  a^3*r^3 = 64  ====>  (ar)^3 = 64 ===>  ar =  = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next step substitute ar = 4 everywhere into (1). You will get\r\n" );
document.write( "\r\n" );
document.write( "a + 4 + 4r = 14,   or\r\n" );
document.write( "\r\n" );
document.write( "a + 4r = 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Express a = 10-4r  and substitute it into ar = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You will get a quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "(10-4r)*r = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The rest is just arithmetic.\r\n" );
document.write( "

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

\n" );