SOLUTION: Solve the equation by any meathod. {{{a^6 - a^2 = a^4 - 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}
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-> SOLUTION: Solve the equation by any meathod. {{{a^6 - a^2 = a^4 - 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}
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Question 38017: Solve the equation by any meathod. 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} Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website! Here's how I did it...starting from
a^6 - a^2 = a^4 - 1
factor out a^2
a^2(a^4 - 1) = a^4 - 1
Now subtract the right side, and then factor it out
a^2(a^4 - 1) - (a^4 - 1) = 0
(a^4 - 1)(a^2 - 1) = 0
Now solve each.
a^4 - 1 = 0
(a^2 + 1)(a^2 - 1) = 0
(a + i)(a - i)(a + 1)(a - 1) = 0
so that a = ±1 and a = ±i
Solving a^2 - 1 = 0 gives redundant solutions.
