document.write( "Question 399928: Solve equation for all value of ų if ų measure in degrees
\n" ); document.write( "2cos^2ų+2=5cosų\r
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Algebra.Com's Answer #283158 by Tatiana_Stebko(1539) $\"\"$ $\"About$

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$\"2%28cosw%29%5E2%2B2=5cosw\"$
\n" ); document.write( " $\"2%28cosw%29%5E2-5cosw%2B2=0\"$
\n" ); document.write( "make the substitution $\"x=cosw\"$ , x have to be from the interval [-1;1](because cosw always takes values only in the interval[-1;1])
\n" ); document.write( " $\"2x%5E2-5x%2B2=0\"$
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%28-%28-5%29+%2B+sqrt%28+%28-5%29%5E2-4%2A2%2A2+%29%29%2F%282%2A2%29+\"$ or $\"x+=+%28-%28-5%29+-+sqrt%28+%28-5%29%5E2-4%2A2%2A2+%29%29%2F%282%2A2%29+\"$
\n" ); document.write( " $\"x+=+%285+%2B+sqrt%28+9%29%29%2F4+\"$ or $\"x+=+%285+-+sqrt%28+9%29%29%2F4+\"$
\n" ); document.write( " $\"x+=+2\"$ or $\"x+=+1%2F2\"$
\n" ); document.write( " $\"x+=+2\"$ is extraneous root of the equation because it does not belong to the interval [-1;1]
\n" ); document.write( "So $\"x+=+1%2F2\"$ ,
\n" ); document.write( "make the substitution back $\"x=cosw\"$ , $\"cosw=1%2F2\"$
\n" ); document.write( "FORMULA: the solution of eguation $\"cosw=a\"$ is w=+- $\"arccos%28a%29%2B360%2Ak\"$ k is any integer
\n" ); document.write( "w=+- $\"arccos%281%2F2%29%2B360%2Ak\"$ k is any integer
\n" ); document.write( "w=+- $\"60%2B360%2Ak\"$ k is any integer \n" ); document.write( "

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