document.write( "Question 1127154: Hi, \r
\n" ); document.write( "\n" ); document.write( "Please help me solve this equation involving negative rational exponents: $\"+3z%5E-1-3z%5E%28-1%2F2%29%2B1=+0+\"$ . \r
\n" ); document.write( "\n" ); document.write( "Here are the steps I took to try to solve the problem:\r
\n" ); document.write( "\n" ); document.write( "First, I used the substitution method using \"u\" and tried completing the square and got $\"+12u%5E2-12u%2B4=+0+\"$ .
\n" ); document.write( "Then, I used the quadratic equation and got 1/ 2 plus or minus 3i sqrt( 3 ) / 2.
\n" ); document.write( "Last I tried solving for x^-1/2 to get the final answer, but I cannot yield the books' answer: 3 / 2 plus or minus 3i sqrt( 3 ) / 2. \r
\n" ); document.write( "\n" ); document.write( "Can you please help me know where I am going wrong? Thank you. \n" ); document.write( "

Algebra.Com's Answer #743524 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The equation is\r\n" );
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document.write( " -  + 1 = 0.\r\n" );
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document.write( "Multiply by z both sides. You will get\r\n" );
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document.write( " = 0,   or, equivalently,\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Now introduce new variable  u = .  The last equation will take the form\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Apply the quadratic formula\r\n" );
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document.write( " =  =  = .\r\n" );
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document.write( "Now consider separately both cases\r\n" );
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document.write( "a)  u =  = .  Hence, squaring, you get\r\n" );
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document.write( "    z =  =  =  = ,    \r\n" );
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document.write( "and\r\n" );
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document.write( "b)  u =  = .  Hence, squaring, you get\r\n" );
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document.write( "    z =  =  =  = .\r\n" );
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document.write( "Answer.  There are two solutions.  They are complex numbers\r\n" );
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document.write( "           and  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Surely, it can be done in many ways and on different paths.\r
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\n" ); document.write( "\n" ); document.write( "I showed here one of the simplest paths/ways.\r
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\n" ); document.write( "\n" ); document.write( "Other people may prefer other ways.\r
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