document.write( "Question 1207740: Let a and b be real numbers. For this problem, assume that a - b = 4 and a^2 - b^2 = 8.\r
\n" ); document.write( "\n" ); document.write( "(a) Find all possible values of ab
\n" ); document.write( "(b) Find all possible values of a+b
\n" ); document.write( "(c) Find all possible values of a and b \n" ); document.write( "

Algebra.Com's Answer #845775 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Let a and b be real numbers. For this problem, assume that a - b = 4 and a^2 - b^2 = 8.
\n" ); document.write( "(a) Find all possible values of ab
\n" ); document.write( "(b) Find all possible values of a+b
\n" ); document.write( "(c) Find all possible values of a and b
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Factor a^2- b^2 = 8 into\r\n" );
document.write( "\r\n" );
document.write( "    (a-b)*(a+b) = 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Replace here a-b by 4, since it is given.  You will get\r\n" );
document.write( "\r\n" );
document.write( "    4*(a+b) = 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies \r\n" );
document.write( "\r\n" );
document.write( "    a + b = 8/4 = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now you have two linear equations for \"a\" and \"b\"\r\n" );
document.write( "\r\n" );
document.write( "    a + b = 2,\r\n" );
document.write( "\r\n" );
document.write( "    a - b = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add them and get  2a = 6;  hence  a = 6/2 = 3.\r\n" );
document.write( "\r\n" );
document.write( "Subtract them and get  2b = 2 - 4 = -2;  hence  b = -2/2 = -1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now  ab = 3*(-1) = -3;        <---- answer to (a)\r\n" );
document.write( "\r\n" );
document.write( "     a + b = 3 + (-1) = 2;    <---- answer to (b)\r\n" );
document.write( "\r\n" );
document.write( "     a = 3;  b = -1.          <---- answer to (c).\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" );