document.write( "Question 1057311: This involves negative exponents and \"equations quadratic in form.\" The equation is:
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document.write( "x^-4 - 10^-2 + 9 = 0 (those are negative exponents: x to the negative fourth power, etc.)
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document.write( "To make solving easier, a substitution is used. Let u = x^-2, and rewrite the original equation as a quadratic equation:
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document.write( "u^2 - 10u + 9 = 0
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document.write( "Factor: (u-1)(u-9) = 0
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document.write( "Apply the zero-product principle: u-1 = 0 or u-9 = 0; so:
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document.write( " u = 1 or u = 9
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document.write( "Now replace u with x^-2 in each of the above equations:
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document.write( "x^-2 = 1 or x^-2 = 9.
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document.write( "Get rid of the negative exponents:
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document.write( "1/x^2 = 1 or 1/x^2 = 9\r
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document.write( "And now here is where I get confused. At this point, my professor writes this on the board as the next step:\r
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document.write( "x^2 = 1 or x^2 = 1/9\r
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document.write( "I have no idea how he got from the previous step to this step. \r
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document.write( "From here, he goes on to apply the square root property:\r
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document.write( "x = +-1 or x = +-1/3
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document.write( "This is the final answer.\r
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document.write( "So my question is:
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document.write( "How do we get from
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document.write( "1/x^2 = 1 or 1/x^2 = 9
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document.write( "to\r
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document.write( "x^2 = 1 or x^2 = 1/9
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document.write( "?
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document.write( "Thank you for any help you can give, and my apologies for the long question.
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Algebra.Com's Answer #672365 by ikleyn(52813)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( "So my question is: \n" ); document.write( "How do we get from \n" ); document.write( "1/x^2 = 1 or 1/x^2 = 9 \n" ); document.write( "to \n" ); document.write( "x^2 = 1 or x^2 = 1/9 \n" ); document.write( "? \n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "If\n" ); document.write( " |