document.write( "Question 1116475: Solve (2x-1)^4 + (2x-1)^2 - 6 = 0 \n" ); document.write( "

Algebra.Com's Answer #731426 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+%282x-1%29%5E4+%2B+%282x-1%29%5E2+-+6+=+0+\"$ \r
\n" ); document.write( "\n" ); document.write( "Let $\"+u+=+%282x-1%29%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+u%5E2+%2B+u+-+6+=+0+\"$
\n" ); document.write( " $\"+%28u-2%29%28u%2B3%29+=+0+\"$ \r
\n" ); document.write( "\n" ); document.write( "u=2 and u=-3 are solutions, consider each in turn:
\r
\n" ); document.write( "\n" ); document.write( "u=2: $\"+%282x-1%29%5E2+=+2+\"$
\n" ); document.write( " $\"+4x%5E2+-+4x+%2B+1+=+2+\"$
\n" ); document.write( " $\"+4x%5E2+-+4x+-+1++=+0+\"$
\n" ); document.write( " $\"+x%5E2+-+x+-+%281%2F4%29+=+0+\"$
\n" ); document.write( " $\"+x%5E2+-+x+++=+%281%2F4%29+\"$
\n" ); document.write( " $\"+x%5E2+-+x+%2B+%281%2F4%29++=+%281%2F4%29+%2B+%281%2F4%29+\"$
\n" ); document.write( " $\"+++%28x+-+1%2F2%29%5E2++=+1%2F2+\"$
\n" ); document.write( " $\"++x+-+1%2F2++\"$ = +/- $\"+1%2Fsqrt%282%29++\"$
\n" ); document.write( " $\"++x+\"$ = +/- $\"+sqrt%282%29%2F2+%2B+%281%2F2%29+\"$
\r
\n" ); document.write( "\n" ); document.write( "Two of the four solutions are real solutions:
\n" ); document.write( " $\"+highlight%28++x=+%281-sqrt%282%29%29%2F2+%29+\"$ and $\"highlight%28+x=%281%2Bsqrt%282%29%29%2F2+%29+\"$
\r
\n" ); document.write( "\n" ); document.write( "Now for the complex solutions:
\n" ); document.write( "u=-3: $\"+%282x-1%29%5E2+=+-3+\"$
\n" ); document.write( " $\"++4x%5E2+-+4x+%2B+1+=+-3+\"$
\n" ); document.write( " $\"++4x%5E2+-+4x++=+-4+\"$
\n" ); document.write( " $\"++x%5E2+-+x+=+-1+\"$
\n" ); document.write( " $\"+x%5E2+-x+%2B+1%2F4+=+-3%2F4+\"$
\n" ); document.write( " $\"+%28x-1%2F2%29%5E2+=+-3%2F4+\"$
\n" ); document.write( " $\"+++x-1%2F2+\"$ = +/- $\"+sqrt%283%29i%2F2+\"$
\n" ); document.write( "
\n" ); document.write( "Which has complex solutions:
\n" ); document.write( " $\"++highlight%28+x=+1%2F2+-+i%2A%28sqrt%283%29%2F2%29+%29+\"$ and $\"+highlight%28+x=1%2F2+%2Bi%2A%28sqrt%283%29%2F2%29%29+\"$
\r
\n" ); document.write( "\n" ); document.write( "The four roots together are all of the solutions to the 4th order equation.\r
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