\r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( "\r\n" );
document.write( "To make things easier, let the radicals be letters and only\r\n" );
document.write( "replace them when they get squared: \r\n" );
document.write( "\r\n" );
document.write( "let A = , B = , C = 
\r\n" );
document.write( "\r\n" );
document.write( "then A² = 5x+1, B² = 3x+4, C² = 16x+9 \r\n" );
document.write( "\r\n" );
document.write( "Since A and B are on the same side they will be multiplied, so\r\n" );
document.write( "\r\n" );
document.write( "(AB)² = (5x+1)(3x+4) = 15x² + 23x + 4 \r\n" );
document.write( "\r\n" );
document.write( "The original problem becomes\r\n" );
document.write( " \r\n" );
document.write( " A + B = C \r\n" );
document.write( "\r\n" );
document.write( "Square both sides:\r\n" );
document.write( "\r\n" );
document.write( " (A + B)² = C²\r\n" );
document.write( "\r\n" );
document.write( " A² + 2AB + B² = 16x + 9\r\n" );
document.write( "\r\n" );
document.write( "5x + 1 + 2AB + 3x + 4 = 16x + 9\r\n" );
document.write( "\r\n" );
document.write( " 8x + 5 + 2AB = 16x + 9\r\n" );
document.write( "\r\n" );
document.write( " 2AB = 8x + 4\r\n" );
document.write( "\r\n" );
document.write( " AB = 4x + 2\r\n" );
document.write( " \r\n" );
document.write( " (AB)² = (4x + 2)²\r\n" );
document.write( " \r\n" );
document.write( " 15x² + 23x + 4 = 16x² + 16x + 4 \r\n" );
document.write( "\r\n" );
document.write( " 0 = x² - 7x \r\n" );
document.write( "\r\n" );
document.write( " 0 = x(x - 7)\r\n" );
document.write( "\r\n" );
document.write( " x = 0; x - 7 = 0\r\n" );
document.write( " x = 7\r\n" );
document.write( "\r\n" );
document.write( "We must check both 0 and 7 for irrational solutions: \r\n" );
document.write( "\r\n" );
document.write( "Checking x = 0\r\n" );
document.write( "\r\n" );
document.write( " + = \r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( " 1 + 2 = 3\r\n" );
document.write( " 3 = 3\r\n" );
document.write( "\r\n" );
document.write( "So x = 0 is a solution \r\n" );
document.write( "\r\n" );
document.write( "Checking x = 7\r\n" );
document.write( "\r\n" );
document.write( " + = \r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( " 
+ 
= 
\r\n" );
document.write( " 6 + 5 = 11\r\n" );
document.write( " 11 = 11\r\n" );
document.write( "\r\n" );
document.write( "So x = 7 is also a solution\r\n" );
document.write( "\r\n" );
document.write( "So x = 0 and x = 7 are the solutions. \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
