document.write( "Question 730422: Please help me solve this equation: x^8-20x^4+64=0 \n" ); document.write( "

Algebra.Com's Answer #446675 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+x%5E8+-+20x%5E4+%2B+64+=+0+\"$
\n" ); document.write( "Let $\"+z%5E2+=+x%5E8+\"$
\n" ); document.write( "and $\"+z+=+x%5E4+\"$
\n" ); document.write( " $\"+z%5E2+-+20z+%2B+64+=+0+\"$
\n" ); document.write( " $\"+%28+z+-+4+%29%2A%28+z+-+16+%29+\"$ ( just figured it out )
\n" ); document.write( " $\"+z+=+4+\"$
\n" ); document.write( " $\"+z+=+16+\"$
\n" ); document.write( "so
\n" ); document.write( " $\"+x%5E4+=+4+\"$
\n" ); document.write( " $\"+x%5E2+=+2+\"$
\n" ); document.write( " $\"+x%5E2+=+-2+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x%5E4+=+16+\"$
\n" ); document.write( " $\"+x%5E2+=+4+\"$
\n" ); document.write( " $\"+x%5E2+=+-4+\"$
\n" ); document.write( "-------------
\n" ); document.write( "Solving for $\"+x+\"$ ,
\n" ); document.write( "(1) $\"+x+=+sqrt%282%29+\"$
\n" ); document.write( "(2) $\"+x+=+-sqrt%282%29+\"$
\n" ); document.write( "(3) $\"+x+=+sqrt%282%29%2Ai+\"$
\n" ); document.write( "(4) $\"+x+=+-sqrt%282%29%2Ai+\"$
\n" ); document.write( "----------------
\n" ); document.write( "(5) $\"+x+=+2+\"$
\n" ); document.write( "(6) $\"+x=+-2+\"$
\n" ); document.write( "(7) $\"+x+=+2i+\"$
\n" ); document.write( "(8) $\"+x+=+-2i+\"$
\n" ); document.write( "The 8 roots are labeled (1) - (8)
\n" ); document.write( "---------------------------
\n" ); document.write( "I'll check one of them
\n" ); document.write( "(4) $\"+x+=+-sqrt%28-2%29+\"$
\n" ); document.write( " $\"+x%5E8+-+20x%5E4+%2B+64+=+0+\"$
\n" ); document.write( " $\"+%28+-sqrt%28-2%29++%29%5E8+-+20%2A%28+-sqrt%28-2%29+%29%5E4+%2B+64+=+0+\"$
\n" ); document.write( " $\"+16%2Ai%5E8+-+20%2A4%2Ai%5E4+%2B+64+=+0+\"$
\n" ); document.write( " $\"+16%2A%28-1%29%5E4+-+80%2A%28-1%29%5E2+%2B+64+=+0+\"$
\n" ); document.write( " $\"+16+-+80+%2B+64+=+0+\"$
\n" ); document.write( " $\"+0+=+0+\"$
\n" ); document.write( "OK
\n" ); document.write( "You can check the rest\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );