document.write( "Question 1104382: if m - 1/m = 5; find:\r
\n" ); document.write( "\n" ); document.write( "(i) m^2 + 1/m^2
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\n" ); document.write( "\n" ); document.write( "I solved the first two but I am unable to solve no. (iii). \n" ); document.write( "

Algebra.Com's Answer #719167 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "I will solve (iii) only.\r
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document.write( " = 5  ====>\r\n" );
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document.write( "m^2 - 5m - 1 = 0  ====>  (apply the quadratic formula)\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "In other words,    = ,   = .\r\n" );
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document.write( "Notice that    = -1.\r\n" );
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document.write( "You can check it by making direct calculations\r\n" );
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document.write( "    =  =  =  = -1,\r\n" );
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document.write( "or derive it from the Vieta's theorem.\r\n" );
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document.write( "Thus   =  =    and   =  = .\r\n" );
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document.write( "It implies    =  =  =  =  = ,   and\r\n" );
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document.write( "              =  =  =  =  = .\r\n" );
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document.write( "Thus you have\r\n" );
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document.write( "             = ,   = ,  which implies   -  = ,   and\r\n" );
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document.write( "             = ,   = ,  which implies   -  = ,\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. If $\"m\"$ - $\"1%2Fm\"$ = 5, then this equation has TWO solutions; correspondingly, \"m\" has TWO values; \r
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\n" ); document.write( "\n" ); document.write( " correspondingly, $\"m%5E2\"$ has TWO values, and, correspondingly, $\"m%5E2\"$ - $\"1%2Fm%5E2\"$ has two values +/- $\"5%2Asqrt%2829%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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