document.write( "Question 1154151: Find three consecutive positive odd integers such that the sum of their squares is 371. \n" ); document.write( "

Algebra.Com's Answer #853817 by ikleyn(53618) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find three consecutive positive odd integers such that the sum of their squares is 371.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I will show another way to calculate.\r
\n" ); document.write( "\n" ); document.write( " It requires less calculations and is much more educative than shown by the other person.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let n be the central number, so the numbers are (n-2), n and (n+2).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Our equation is\r\n" );
document.write( "\r\n" );
document.write( "    (n-2)^2 + n^2 + (n+2)^2 = 371.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and find 'n'\r\n" );
document.write( "\r\n" );
document.write( "    (n^2 - 4n + 4) + n^2 + (n^2 + 4n + 4) = 371\r\n" );
document.write( "\r\n" );
document.write( "     3n^2 + 8 = 371\r\n" );
document.write( "\r\n" );
document.write( "     3n^2 = 371 - 8 = 363\r\n" );
document.write( "\r\n" );
document.write( "      n^2 = 363/3 = 121\r\n" );
document.write( "\r\n" );
document.write( "      n =  = +/- 11.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We are looking for positive integers, so n = 11,  and the numbers are 9, 11, 13.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is how this problem is EXPECTED to be solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );