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March 27, 2017

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what is the factor of a^4-7a^2+9 ?

  • math - ,

    a^4-7a^2+9
    a^2 = (7±√13)/2

    Now it gets tricky:

    7+√13 = (1+2√13+13)/2 = (1+√13)^2/2

    So, if
    a^2 = (7+√13)/2 = (1+√13)^2/4
    a = ±1/2 (√13+1)
    and
    a = ±1/2 (√13-1)

    Makes things kind of nasty, the factors are

    1/16 (±2x + √13 ± 1)

    where all 4 combinations of + and - are used.

  • math - ,

    Hint:
    substitute u=a^2, then
    a^4-7a^2+9
    =u^2-7u+9
    and try to factorize.

    However, check you question to see if there is a typo. The above expression in u does not have rational factors.

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