document.write( "Question 911429: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
\n" ); document.write( "8 cos3 x = 8 cos x
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Algebra.Com's Answer #553243 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"8%2Acos%283x%29+=+8%2Acos%28x%29\"$
\n" ); document.write( " $\"cos%283x%29=cos%28x%29\"$
\n" ); document.write( " $\"4cos%5E3%28x%29-3cos%28x%29=cos%28x%29\"$
\n" ); document.write( "Let $\"u=cos%28x%29\"$
\n" ); document.write( " $\"4u%5E3-3u=u\"$
\n" ); document.write( " $\"4u%5E3-4u=0\"$
\n" ); document.write( " $\"u%28u%5E2-1%29=0\"$
\n" ); document.write( " $\"u%28u%2B1%29%28u-1%29=0\"$
\n" ); document.write( "Three solutions,
\n" ); document.write( " $\"u=0\"$
\n" ); document.write( " $\"cos%28x%29=0\"$
\n" ); document.write( " $\"x=pi%2F2\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"u%2B1=0\"$
\n" ); document.write( " $\"u=-1\"$
\n" ); document.write( " $\"cos%28x%29=-1\"$
\n" ); document.write( " $\"x=pi\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"u-1=0\"$
\n" ); document.write( " $\"u=1\"$
\n" ); document.write( " $\"cos%28x%29=1\"$
\n" ); document.write( " $\"x=0\"$
\n" ); document.write( ".
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\n" ); document.write( ".
\n" ); document.write( " $\"0\"$ , $\"pi%2F2\"$ , $\"pi\"$ \n" ); document.write( "

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