document.write( "Question 947349: a. Jull wants to make a substitution in the equation: x^(1/3)-36=9x^(1/6) in order to convert it to a quadratic equation. Give the substitution (in form t=...) and the resulting quadratic equation. Do not solve.\r
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Algebra.Com's Answer #578018 by MathTherapy(10552)\"\" \"About 
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\n" ); document.write( "a. Jull wants to make a substitution in the equation: x^(1/3)-36=9x^(1/6) in order to convert it to a quadratic equation. Give the substitution (in form t=...) and the resulting quadratic equation. Do not solve.\r
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\"highlight%28highlight%28x%5E%281%2F3%29+-+36+=+9x%5E%281%2F6%29%29%29\"
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document.write( "\"highlight%28highlight%28x%5E%281%2F3%29+-+9x%5E%281%2F6%29+-+36+=+0%29%29\"\r
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document.write( "Let \"highlight%28highlight%28t+=+x%5E%281%2F6%29%29%29\"
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document.write( "Then \"t%5E2+=+%28x%5E%281%2F6%29%29%5E2\", or \"highlight%28highlight%28t%5E%281%2F3%29%29%29\"
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document.write( "\"highlight%28highlight%28x%5E%281%2F3%29+-+9x%5E%281%2F6%29+-+36+=+0%29%29\" becomes: \"t%5E2+-+9t+-+36+=+0\" ------- Resulting quadratic equation after substitution of t for \"highlight%28highlight%28x%5E%281%2F6%29%29%29\"\r
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document.write( "b.
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document.write( "Since \"u+=+x%5E4\", and u = 16, and u = - 4\r
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document.write( "\"u+=+x%5E4\", with u = 16
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document.write( "\"16+=+x%5E4\" 
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document.write( "\"2%5E4+=+x%5E4\" 
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document.write( "Thus, \"highlight_green%282+=+x%29\"\r
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document.write( "\"u+=+x%5E4\", with u = - 4 
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document.write( "\"-+4+=+x%5E4\" 
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document.write( "This is an EXTRANEOUS SOLUTION, since NO EXPRESSION raised to a power results in a negative (< 0) value  \r
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document.write( "Therefore, only solution is: \"highlight_green%28x+=+2%29\" \n" );
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