document.write( "Question 1171175: What is the difference (y-x) if:
\n" ); document.write( "
\n" ); document.write( "6x + 5y + √(6x + 5y) = 72\r
\n" ); document.write( "\n" ); document.write( "3x - 4y + √(3x - 4y) = 30 \n" ); document.write( "

Algebra.Com's Answer #796094 by ikleyn(52858) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " First, we accept the agreement that we consider only positive values of the square roots.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " After that, we solve the problem in several steps.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Step 1.  We find 6x + 5y from the first equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = 72.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    For it, we introduce new variable u = .\r\n" );
document.write( "\r\n" );
document.write( "    Then the equation takes the form\r\n" );
document.write( "\r\n" );
document.write( "         u^2 + u = 72\r\n" );
document.write( "\r\n" );
document.write( "         u^2 + u - 72 = 0\r\n" );
document.write( "\r\n" );
document.write( "         (u+9)*(u-8) = 0.\r\n" );
document.write( "\r\n" );
document.write( "     The roots are -9 and 8, but we accept only positive root  u= 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Then we have THIS equation \r\n" );
document.write( "\r\n" );
document.write( "         6x + 5y = ,   or\r\n" );
document.write( "\r\n" );
document.write( "         6x + 5y = 64.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Step 1 is complete.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 2.  We find 3x - 4y from the second equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = 30.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    For it, we introduce new variable v = .\r\n" );
document.write( "\r\n" );
document.write( "    Then the equation takes the form\r\n" );
document.write( "\r\n" );
document.write( "         v^2 + v = 30\r\n" );
document.write( "\r\n" );
document.write( "         v^2 + v - 30 = 0\r\n" );
document.write( "\r\n" );
document.write( "         (v+6)*(v-5) = 0.\r\n" );
document.write( "\r\n" );
document.write( "     The roots are -6 and 5, but we accept only positive root  v= 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Then we have THIS equation \r\n" );
document.write( "\r\n" );
document.write( "         3x - 5y = ,   or\r\n" );
document.write( "\r\n" );
document.write( "         3x - 5y = 25.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Step 2 is complete.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 3.  Solving the system (1), (2) to find x and y.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The system is\r\n" );
document.write( "\r\n" );
document.write( "         6x + 5y = 64.    (1)\r\n" );
document.write( "\r\n" );
document.write( "         3x - 5y = 25.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Solve it by ANY WAY you know / (you like) / (you prefer).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The solution is  x = ;  y = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Step 4.  Calculate  y - x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    It is    y - x =  -  =  = -8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution is completed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The   ANSWER   is   y - x = -8.\r\n" );
document.write( "

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

\n" );