document.write( "Question 1130004: Solve the equation (y+5/y)^2 + 3(y+5/y)=4 ,using substitution u=y+5/y \n" ); document.write( "

Algebra.Com's Answer #746652 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Solve the equation (y+5/y)^2 + 3(y+5/y)=4 ,using substitution u=y+5/y
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document.write( "When you introduce new variable  u = , the original equation takes the form\r\n" );
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document.write( "u^2 + 3u - 4 = 0.\r\n" );
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document.write( "Factoring, you get\r\n" );
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document.write( "(u+4)*(u-1) = 0,\r\n" );
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document.write( "which gives you two roots  u= -4  and  u= 1.\r\n" );
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document.write( "Thus, now you need to solve two equations   = -4  and   = 1 to find possible solutions for \"y\".\r\n" );
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document.write( "1)   = -4  <====> is equivalent to\r\n" );
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document.write( "     = 0  <=====>  is equivalent to\r\n" );
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document.write( "     = 0   or    = -1\r\n" );
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document.write( "                              which has no solutions in real numbers,\r\n" );
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document.write( "    but has two solutions in complex numbers  x= -2 + i  and  x= -2 -i.  \r\n" );
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document.write( "2)   = 1  <====> is equivalent to\r\n" );
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document.write( "     = 0  <=====>  is equivalent to\r\n" );
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document.write( "     = 0   or    = -4.75,\r\n" );
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document.write( "                              which has no solutions in real numbers,\r\n" );
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document.write( "    but has two solutions in complex numbers  x=   and  x= .\r\n" );
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document.write( "Answer.  Your original equation has no solution/solutions in real numbers, but has 4 (four) solutions in complex numbers, listed above.\r\n" );
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