document.write( "Question 1208747: Find two consecutive positive integers such that the square of the first
\n" ); document.write( "increased by 2 times the second is equal to 37.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #847181 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find two consecutive positive integers such that the square of the first
\n" ); document.write( "increased by 2 times the second is equal to 37.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let first (smaller) positive integer be n; then the next consecutive integer number is (n+1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Write an equation according to the problem\r\n" );
document.write( "\r\n" );
document.write( "    n^2 + 2*(n+1) = 37.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "    n^2 + 2n + 2 = 37,\r\n" );
document.write( "\r\n" );
document.write( "    n^2 + 2n - 35 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factorize\r\n" );
document.write( "\r\n" );
document.write( "    (n+7)*(n-5) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The roots are n= -7  and  n= 5.   We want the positive value.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The numbers are 5 and 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  5^2 + 2*6 = 25 + 12 = 37.    ! correct !\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( "/////////////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Based on Edwin's note, someone can write a Master thesis or even a PhD dissertation in Math education :).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As an epigraph to such a Master thesis or PhD dissertation the person may write
\n" ); document.write( "that word problems in English often require a small auxiliary volume of explanations
\n" ); document.write( "of used terms and of what exactly means by the author, and what does not mean.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );