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March 30, 2017

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Solve by any method.

a^4 – 5a^2 + 4 = 0


I am having problems figuring out what method to use to solve this problem. I need to show my steps and I am not sure how to do this. Can someone help? Thanks.

  • College Math II - ,

    This equation can be solved by factoring. Have you learned how to do that yet? You should have.

    This is not college level math. It is taught in the ninth grade

    Hint: one of the factors is (a-4)

  • College Math II (correction) - ,

    OK, I made a mistake. Sorry about that. I didn't notice that is was fourth order.

    The factors are:

    (a^2-2)(a^2 +2)
    which can be factored again to give
    (a + sqrt2)(a - sqrt2)(a + isqrt2)(a - isqrt2)

    Set that equal to zero and you will see that you have an answer whenever one of the factors is zero.
    (i is the square root of -1)

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