document.write( "Question 855999: Solve for all real values of x in radians. $\"2cos%5E2x-5cosx%2B2=0\"$ \n" ); document.write( "

Algebra.Com's Answer #515675 by KMST(5328) $\"\"$ $\"About$

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$\"2cos%5E2%28x%29-5cos%28x%29%2B2=0\"$ meaning $\"2%28cos%28x%29%29%5E2-5cos%28x%29%2B2=0\"$
\n" ); document.write( "is easier to solve by thinking in terms of
\n" ); document.write( " $\"y=cos%28x%29\"$ and seeing the equation as
\n" ); document.write( " $\"2y%5E2-5y%2B2=0\"$
\n" ); document.write( "The solutions to that equation (no matter how you find them) are
\n" ); document.write( " $\"y=2\"$ and $\"y=1%2F2\"$
\n" ); document.write( "Going back to $\"x\"$ , $\"cox%28x%29=2\"$ has no solution,
\n" ); document.write( "but $\"cos%28x%29=1%2F2\"$ has an infinite number of solutions.
\n" ); document.write( "In the first quadrant, $\"cos%28pi%2F3%29=1%2F2\"$ ,
\n" ); document.write( "and in the fourth quadrant $\"cos%28-pi%2F3%29=1%2F2\"$ .
\n" ); document.write( "Adding those solutions plus all the co-terminal angles differing from those by an integer number of turns,
\n" ); document.write( "we can express all the solutions as
\n" ); document.write( " $\"2n%2Api+%2B-+pi%2F3\"$ or maybe even $\"%282n%2B1%2F3%29pi\"$ . \n" ); document.write( "

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