document.write( "Question 38017: Solve the equation by any meathod. \"a%5E6+-+a%5E2+=+a%5E4+-+1\" I'm not sure if I'm supposed to move it all to one side, or what I'm so confused, the answer is {+-1,+-i} \n" ); document.write( "
Algebra.Com's Answer #23560 by fractalier(6550)\"\" \"About 
You can put this solution on YOUR website!
Here's how I did it...starting from
\n" ); document.write( "a^6 - a^2 = a^4 - 1
\n" ); document.write( "factor out a^2
\n" ); document.write( "a^2(a^4 - 1) = a^4 - 1
\n" ); document.write( "Now subtract the right side, and then factor it out
\n" ); document.write( "a^2(a^4 - 1) - (a^4 - 1) = 0\r
\n" ); document.write( "\n" ); document.write( "(a^4 - 1)(a^2 - 1) = 0
\n" ); document.write( "Now solve each.
\n" ); document.write( "a^4 - 1 = 0
\n" ); document.write( "(a^2 + 1)(a^2 - 1) = 0
\n" ); document.write( "(a + i)(a - i)(a + 1)(a - 1) = 0
\n" ); document.write( "so that a = ±1 and a = ±i
\n" ); document.write( "Solving a^2 - 1 = 0 gives redundant solutions. \n" ); document.write( "
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