document.write( "Question 1046294: Kindly help me solving it
\n" ); document.write( "What are the roots obtained by solving equation
\n" ); document.write( " $\"z%5E2-6z%2B9=4+%28z%5E2-6z%2B6%29%5E%281%2F2%29\"$ ?
\n" ); document.write( "Well i tried hard and simplified it upto
\n" ); document.write( " $\"z%5E4-12z%5E3%2B38z%5E2-12z%2B63=0\"$
\n" ); document.write( "But i can't go further, so please guide me. \n" ); document.write( "

Algebra.Com's Answer #661788 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Kindly help me solving it
\n" ); document.write( "What are the roots obtained by solving equation
\n" ); document.write( " $\"z%5E2-6z%2B9=4+%28z%5E2-6z%2B6%29%5E%281%2F2%29\"$ ?
\n" ); document.write( "Well i tried hard and simplified it upto
\n" ); document.write( " $\"z%5E4-12z%5E3%2B38z%5E2-12z%2B63=0\"$
\n" ); document.write( "But i can't go further, so please guide me.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "Rewrite equivalently\r\n" );
document.write( "\r\n" );
document.write( " = .\r\n" );
document.write( "\r\n" );
document.write( "Square both sides:\r\n" );
document.write( "\r\n" );
document.write( " = .\r\n" );
document.write( "\r\n" );
document.write( "Introduce new variable x = . The last equation takes the form\r\n" );
document.write( "\r\n" );
document.write( " = ,  or\r\n" );
document.write( "\r\n" );
document.write( " = .\r\n" );
document.write( "\r\n" );
document.write( "Solve by any way (factoring or the quadratic formula). You will get the roots\r\n" );
document.write( "\r\n" );
document.write( "  x = 12  and/or  x = 4.\r\n" );
document.write( "\r\n" );
document.write( "Thus you have two options:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1.  {z-3)^2 = 4   --->  z-3 = 2  or  z-3 = -2  --->  z = 5  or  z = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  (z-3)^2 = 12  --->  z-3 = +/- = +/-  --->  z =   and/or  z = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check that all these roots are the solutions of the original equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer. The solutions are  z = 1,  z = 5,  z = ,  z = .\r\n" );
document.write( "

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

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

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plots y = $\"x%5E2-6x%2B9\"$ (red), y = $\"4%2Asqrt%28x%5E2-6x%2B6%29\"$ (green)\r
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );