document.write( "Question 339921: Solve by introducing a substitution that transforms these equations to quadratic form\r
\n" ); document.write( "\n" ); document.write( "x^(-8)-17x^(-4)+16=0 \n" ); document.write( "

Algebra.Com's Answer #243955 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"u=x%5E%28-4%29\"$ , then $\"u%5E2=x%5E%28-8%29\"$ ,
\n" ); document.write( " $\"u%5E2-17u%2B16=0\"$
\n" ); document.write( " $\"%28u-1%29%28u-16%29=0\"$
\n" ); document.write( "Two u solutions:
\n" ); document.write( " $\"u-1=0\"$
\n" ); document.write( " $\"u=1\"$
\n" ); document.write( " $\"x%5E%28-4%29=1\"$
\n" ); document.write( " $\"x%5E%284%29=1\"$
\n" ); document.write( " $\"x%5E4-1=0\"$
\n" ); document.write( " $\"%28x%5E2-1%29%28x%5E2%2B1%29=0\"$
\n" ); document.write( " $\"%28x-1%29%28x%2B1%29%28x%5E2%2B1%29=0\"$
\n" ); document.write( "Four x solutions: x= $\"-1\"$ , $\"1\"$ , $\"-i\"$ , $\"i\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"u-16=0\"$
\n" ); document.write( " $\"u=16\"$
\n" ); document.write( " $\"x%5E%28-4%29=16\"$
\n" ); document.write( " $\"x%5E%284%29=1%2F16\"$
\n" ); document.write( " $\"x%5E4-1%2F16=0\"$
\n" ); document.write( " $\"%28x%5E2-1%2F4%29%28x%5E2%2B1%2F4%29=0\"$
\n" ); document.write( " $\"%28x-1%2F2%29%28x%2B1%2F2%29%28x%5E2%2B1%2F4%29=0\"$
\n" ); document.write( "Four x solutions: x= $\"-1%2F2\"$ , $\"1%2F2\"$ , $\"-%281%2F2%29i\"$ , $\"%281%2F2%29i\"$
\n" ); document.write( " \n" ); document.write( "

\n" );