document.write( "Question 1126756: Ix x>0, y>0 and $\"x%5E2+-y%5E2+=2xy\"$ , find the exact value of $\"x%2Fy\"$ . \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Thanks. \n" ); document.write( "

Algebra.Com's Answer #743090 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The original equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     -  = 2xy.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by    (which is not zero !).  You will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     - 1 = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Introduce new variable  t = .   Then the last equation takes the form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     - 2t - 1 = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is a quadratic equation on t. Solve it using the quadratic formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The ratio  ,  where x > 0 and y > 0 satisfy the given equation, is  .\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Naturally, this solution has N O T H I N G    C O M M O N with the answer and solution by @josgarithmetic, \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "whose post is   T O T A L L Y   I R R E L E V A N T to the given problem.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As usual.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "@josgarithmetic is VERY well known (or better to say, very badly known, unfortunately) in this forum,
\n" ); document.write( "for his inability to solve problems correctly and to make calculations accurately.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So be very careful when you obtain \"solutions\" from him.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In half of all cases (if not at most cases) they are wrong.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do not trust him and always wait for reaction of other tutors.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In the normal school environment he would be fired in the second day.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I think about thousands of visitors and students who do understand almost nothing in Math and who were misguided
\n" ); document.write( "by his false and wrong quasi- and pseudo-\"solutions\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "People, be careful about @josgarithmetic !   !    !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );