document.write( "Question 829436: 9x^(2/3)+4x^(-2/3)=37. Find x. \n" ); document.write( "

Algebra.Com's Answer #499894 by Fombitz(32388) $\"\"$ $\"About$

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Let $\"u=x%5E%281%2F3%29\"$
\n" ); document.write( " $\"9x%5E%282%2F3%29%2B4x%5E%28-2%2F3%29=37\"$
\n" ); document.write( "Mutliply both sides by $\"x%5E%282%2F3%29\"$
\n" ); document.write( " $\"9x%5E%284%2F3%29%2B4=37x%5E%282%2F3%29\"$
\n" ); document.write( " $\"9x%5E%284%2F3%29-37x%5E%282%2F3%29%2B4=0\"$
\n" ); document.write( "Substitute $\"u=x%5E%282%2F3%29\"$
\n" ); document.write( " $\"9u%5E2-37u%2B4=0\"$
\n" ); document.write( " $\"%289u-1%29%28u-4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"9u-1=0\"$
\n" ); document.write( " $\"9u=1\"$
\n" ); document.write( " $\"u=1%2F9\"$
\n" ); document.write( " $\"x%5E%282%2F3%29=1%2F9\"$
\n" ); document.write( " $\"highlight%28x=1%2F27%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"u-4=0\"$
\n" ); document.write( " $\"u=4\"$
\n" ); document.write( " $\"x%5E%282%2F3%29=4\"$
\n" ); document.write( " $\"x=4%5E%283%2F2%29\"$
\n" ); document.write( " $\"highlight%28x=8%29\"$
\n" ); document.write( "Now check the solution in the original equation to verify that it works.
\n" ); document.write( " \n" ); document.write( "

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